Sequences (Edexcel IGCSE Maths)

Exam Questions

3 hours41 questions
1
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1 mark

The first four terms of a sequence are    –10    –8    –6    –4

Circle the expression for the n spaceth term of the sequence.

– 12 space – space 2 n – 8 space – space 2 n n space plus space 2 2 n space – space 12

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2
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1 mark

The first 4 terms of a linear sequence are

      3    11    19    27

Circle the expression for the nth term.

8 space – space 5 n n space plus space 8 8 n space plus space 3 8 n space – space 5

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3
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2 marks

Write an expression for thespace nth term of the sequence below.

15    12    9    6

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4
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1 mark

A sequence is defined using this term-to-term rule.

u subscript n plus 1 end subscript space equals space square root of 2 u subscript n plus space 15 end root

If u subscript 1 space equals space 5, find u subscript 2

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5
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1 mark

Here is a sequence of numbers.

7,   5,   3,   1,   – 1, …

Find the next term in this sequence.

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6
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1 mark

These are the first five terms in a sequence.
 

8 space space space space space 11 space space space space space 14 space space space space space 17 space space space space space 20


Find the next term.

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1a
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2 marks

Here are the first 5 terms of an arithmetic sequence.

3     9   15   21   27

Find an expression, in terms of n, for the nth term of this sequence.

1b
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1 mark

Ben says that 150 is in the sequence.

Is Ben right?

You must explain your answer.

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2a
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2 marks

Here are the first four terms of an arithmetic sequence.

3   10   17   24

Find, in terms of n, an expression for the nth term of this arithmetic sequence.

2b
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2 marks

Is 150 a term of this sequence?

You must explain how you get your answer.

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3a
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2 marks

Here are the first five terms of an arithmetic sequence.

2   6   10   14   18

Write down an expression, in terms of n, for the nth term of this sequence.

3b
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1 mark

Is 86 a term in the sequence?

You must give a reason for your answer.

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4a
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2 marks

Here are the first four terms of an arithmetic sequence.

11   17   23   29

Find, in terms of n, an expression for the nth term of this arithmetic sequence.

4b
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2 marks

Is 121 a term of this arithmetic sequence?
You must explain your answer.

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5a
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2 marks

Here are the first four terms of an arithmetic sequence.

6   10   14   18

Write an expression, in terms of n, for the nth term of this sequence.

5b
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2 marks

The nth term of a different arithmetic sequence is 3 n space plus space 5

Is 108 a term of this sequence?

Show how you get your answer.

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6a
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2 marks

Here are the first five terms of an arithmetic sequence.

4   9   14   19   24

Find, in terms of n, an expression for the nth term of this sequence.

6b
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1 mark

Here are the first five terms of a different sequence.

2      2      0      -4      -10

An expression for the nth term of this sequence is 3 n space long dash space n squared

Write down, in terms of n, an expression for the nth term of a sequence whose first five terms are  

4      4      0      -8      -20

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7
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2 marks

The  nth term of a number sequence is n2 + 1

Write down the first three terms of the sequence.

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8
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2 marks

Here are the first four terms of a sequence of fractions.

1 over 1 space space space space space space 2 over 3 space space space space space space 3 over 5 space space space space space space space 4 over 7

The numerators of the fractions form the sequence of whole numbers 1 space 2 space 3 space 4 space...
The denominators of the fractions form the sequence of odd numbers 1 space 3 space 5 space 7 space...

Write down an expression, in terms of n, for the n th term of this sequence of fractions.

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9
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2 marks

Here are the first five terms of an arithmetic sequence.

7 10 13 16 19

Find the sum of the first 100 terms of this sequence.

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10a
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2 marks

Here are the first four terms of an arithmetic sequence.

6 space space space space space space space space 10 space space space space space space space space space 14 space space space space space space space space space 18

Find an expression, in terms of n, for the n th term of this sequence.

10b
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1 mark

Write down an expression, in terms of n, for the left parenthesis n space plus space 1 right parenthesis th term of this sequence.

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11a
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2 marks

Here are the first five terms of a number sequence S.

10 space space space space space space space 16 space space space space space space space space 22 space space space space space space space space 28 space space space space space space space space 34

Find an expression, in terms of n, for the n th term of this sequence.

11b
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2 marks

The n th term of a sequence T is given by n squared space minus space 3

There are numbers that are terms in both the sequence S and the sequence T.

Find one of these numbers.

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12a
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2 marks

Here are the first five terms of a number sequence.

7    11    15    19    23

Find an expression, in terms of n , for the nth term of this sequence.

12b
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2 marks

The nth term of a different number sequence is given by 80 space – space 2 n

Write down the first 3 terms of this sequence.

12c
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1 mark

Yuen says there are no numbers that are in both of the sequences.

Yuen is correct.

Explain why.

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13a
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3 marks

A sunflower grows at a rate of 4 cm each day.

How many days does it take to grow from a height of 80 cm to more than 1.06 m?

13b
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1 mark

If the sunflower grows at a faster rate, how would this affect your answer to part (bold a)?

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1a
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1 mark

The nth term of a sequence is a n squared space plus space b n.

Write down an expression, in terms of a and b, for the 3rd term.

1b
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4 marks

The 3rd term of this sequence is 21 and the 6th term is 96.

Find the value of a and the value of b
You must show all your working.

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2a
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2 marks

Here are the first five terms of an arithmetic sequence.

2   5   8   11   14

Write down an expression, in terms of n, for the nth term of this sequence.

2b
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2 marks

Is 299 a term of this sequence?

You must give a reason for your answer.

2c
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1 mark

Write down an expression, in terms of n, for the space left parenthesis n space plus space 1 right parenthesisth term of this sequence.

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3a
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1 mark

In all the following sequences, after the first two terms, the rule is to add the previous two terms to find the next term.

Write down the next two terms in this sequence.
   

1    2    3    5    8    13      ...........      ...........

3b
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2 marks

Write down the first two terms of this sequence.

.............       .............   3    11    14

3c
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8 marks
(i)
Find the value of d and the value of e.

      2    d     e  10

[3]

(ii)
Find the value of x, the value of y and the value of z.


      -33    x    y    z    18

[5]

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4
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4 marks

An arithmetic series has first term 1 and common difference 4.

Find the sum of all terms of the series from the 41st term to the 100th term inclusive.

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5
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5 marks

The sum of the first N terms of an arithmetic series, S, is 292
The 2nd term of S is 8.5
The 5th term of S is 13

Find the value of N.
Show clear algebraic working.

N space equals ...................................................... 

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6
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3 marks

Mario is going to save $50 in the year 2021

He is going to continue to save, up to and including the year 2070, by increasing the amount he saves each year by $ k

Mario will save a total of $33 125 from 2021 to 2070

Work out the value of k.

k equals....................

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7
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4 marks

The first term of an arithmetic series S is –6
The sum of the first 30 terms of S is 2865

Find the 9th term of S.

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8
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4 marks

In an arithmetic series, the 6 th term is 39
In the same arithmetic series, the 19 th term is 7.8

Work out the sum of the first 25 terms of the arithmetic series.

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9
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4 marks

Work out the sum of the multiples of 3 between 1 and 1000

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10
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4 marks

Here are the first five terms of an arithmetic sequence.

8 space space space space space space space 15 space space space space space space space space 22 space space space space space space space space 29 space space space space space space space space 36

Work out the sum of all the terms from the 50 th term to the 100 th term inclusive.

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11
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3 marks

Theo starts with savings of £18
James starts with no savings.

Each week from now,

   Theo will save £4.50 and James will save £4

In how many weeks will Theo and James have savings in the ratio 15 : 8 ?

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12
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5 marks

A sequence is defined using this term-to-term rule,

u subscript n plus 1 end subscript space equals space k u subscript n space plus space r

where k and r are constants.

Given that u subscript 2 space equals space 41 , u subscript 3 space equals space 206 and u subscript 4 space equals space 1031, find the value of k and the value of r.

k space= ................

r = .................

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13
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3 marks

A sequence is defined by the rule u subscript n plus 1 end subscript equals 5 u subscript n minus 15

If u subscript 3 equals 6, calculate

(i)
u subscript 5
u subscript 5=............................[3]

(ii)
u subscript 2
u subscript 2=............................[3]

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1
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4 marks

An arithmetic series has first term a and common difference d.

The sum of the first 2 n terms of the series is four times the sum of the first n terms of the series.

Find an expression for a in terms of d.
Show your working clearly.

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2
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6 marks

The nth term of an arithmetic series is u subscript n where u subscript n space greater than space 0 for all n

The sum to n terms of the series is S subscript n

Given that u subscript 4 space space equals space 6 and that S subscript 11 space end subscript equals space left parenthesis u subscript 6 space right parenthesis squared plus space 18

find the value of u subscript 20

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3
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5 marks

Here are the first four terms of an arithmetic series.

k      fraction numerator 3 k over denominator 4 end fraction     k over 2     k over 4

Given that the 15th term of the series is left parenthesis 90 space plus space 2 k right parenthesis,
calculate the sum of the first 30 terms of the series.

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4
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4 marks

left parenthesis 2 x space plus space 23 right parenthesis comma space left parenthesis 8 x space plus space 2 right parenthesis and left parenthesis 20 x space – space 52 right parenthesis are three consecutive terms of an arithmetic sequence.

Prove that the common difference of the sequence is 12

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5
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5 marks

An arithmetic series has first termspace a and common difference d, where d spaceis a prime number.

The sum of the first n terms of the series is S subscript nand

S subscript m equals 39
S subscript 2 m end subscript space equals space 320

Find the value of d spaceand the value of m
Show clear algebraic working.

table attributes columnalign right center left columnspacing 0px end attributes row d equals cell................... end cell row m equals cell................... end cell end table

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6
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5 marks

The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first 36 terms of the same series.

Find the sum of the first 30 terms of this series.

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7
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5 marks

The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765

Find the 16th term of the arithmetic series.
Show your working clearly.

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8
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4 marks

The 10 th term of an arithmetic series, S, is 66
The sum of the first 20 terms of S is 1290

Find the 5 th term of S.
Show your working clearly.

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9
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5 marks

The 3rd term of an arithmetic series, A , is 19
The sum of the first 10 terms of A is 290

Find the 10th term of A.

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