The th term of a number sequence is
Write down the first three terms of the sequence.
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The th term of a number sequence is
Write down the first three terms of the sequence.
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The first three terms of a geometric progression are
Circle the fourth term.
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The next term of a sequence is made by adding the previous two terms.
Which of these sequences follows this rule?
Circle your answer.
–9 2 –7 –5 –12 | –3 5 –2 3 1 |
0 –3 –3 0 –3 | –1 –1 –2 –3 1 |
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Which of these is a geometric progression?
Circle your answer.
1 3 5 7 9 | 1 3 6 10 15 |
1 4 9 16 25 | 1 3 9 27 81 |
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The first 4 terms of a linear sequence are
3 11 19 27
Circle the expression for the th term.
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Which of these is a geometric progression?
Circle your answer.
2, 4, 6, 8, 10 | 2, 3, 5, 8, 12 |
2, 6, 18, 54, 162 | 2, 6, 10, 14, 18 |
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Which sequence is a geometric progression?
Circle your answer.
1 2 3 4 | 1 2 4 7 |
1 2 4 8 | 1 2 3 5 |
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The first four terms of a sequence are –10 –8 –6 –4
Circle the expression for the th term of the sequence.
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Here is a sequence.
90 | 82 | 74 | 66 | 58 |
Circle the expression for the nth term of the sequence.
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A geometric progression starts 4 16
Work out the next term.
A Fibonacci-type sequence starts 3 –8
The sequence is continued by adding the previous two terms.
Work out the next two terms.
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Write the next term in each of these sequences.
i) 1 1 2 3 5 8
[1]
ii) 2 4 8 16 32 64
[1]
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Write an expression for theth term of the sequence below.
15 12 9 6
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A sequence is defined using this term-to-term rule.
If , find
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This expression can be used to generate a sequence of numbers.
i) Work out the first three terms of this sequence.
[2]
ii) Show that this expression does not only generate prime numbers.
[2]
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Here are the first 5 terms of an arithmetic sequence.
3 9 15 21 27
Find an expression, in terms of , for the
th term of this sequence.
Ben says that 150 is in the sequence.
Is Ben right?
You must explain your answer.
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Here are the first four terms of an arithmetic sequence.
3 10 17 24
Find, in terms of , an expression for the
th term of this arithmetic sequence.
Is 150 a term of this sequence?
You must explain how you get your answer.
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Here are the first five terms of an arithmetic sequence.
2 6 10 14 18
Write down an expression, in terms of , for the
th term of this sequence.
Is 86 a term in the sequence?
You must give a reason for your answer.
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Here are the first four terms of an arithmetic sequence.
11 17 23 29
Find, in terms of , an expression for the
th term of this arithmetic sequence.
Is 121 a term of this arithmetic sequence?
You must explain your answer.
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Here are the first four terms of an arithmetic sequence.
6 10 14 18
Write an expression, in terms of , for the
th term of this sequence.
The th term of a different arithmetic sequence is
Is 108 a term of this sequence?
Show how you get your answer.
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Here are the first five terms of an arithmetic sequence.
4 9 14 19 24
Find, in terms of , an expression for the
th term of this sequence.
Here are the first five terms of a different sequence.
2 2 0 -4 -10
An expression for the th term of this sequence is
Write down, in terms of , an expression for the
th term of a sequence whose first five terms are
4 4 0 -8 -20
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Here are the first six terms of a Fibonacci sequence.
1 1 2 3 5 8
The rule to continue a Fibonacci sequence is,
the next term in the sequence is the sum of the two previous terms.
Find the 9th term of this sequence.
The first three terms of a different Fibonacci sequence are
Show that the th term of this sequence is
Given that the 3rd term is 7 and the 6th term is 29,
find the value of and the value of
.
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Here are the first 5 terms of a quadratic sequence.
1 3 7 13 21
Find an expression, in terms of , for the
th term of this quadratic sequence.
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Find the th term of each of these sequences.
16, 19, 22, 25, 28, ...
1, 3, 9, 27, 81, ...
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The first five terms of a sequence are 4, 9, 16, 25, 36, ..... Find
the 10th term,
the th term.
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Here are the first six terms of a quadratic sequence.
-1 5 15 29 47 69
Find an expression, in terms of , for the
th term of this sequence.
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Here are the first four terms of a sequence of fractions.
The numerators of the fractions form the sequence of whole numbers The denominators of the fractions form the sequence of odd numbers
Write down an expression, in terms of , for the
term of this sequence of fractions.
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Here are the first five terms of a number sequence .
Find an expression, in terms of , for the
term of this sequence.
The term of a sequence
is given by
There are numbers that are terms in both the sequence and the sequence
Find one of these numbers.
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Here are the first four terms of an arithmetic sequence.
Find an expression, in terms of , for the
term of this sequence.
Write down an expression, in terms of , for the
term of this sequence.
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Here are the first five terms of a number sequence.
7 11 15 19 23
Find an expression, in terms of , for the
th term of this sequence.
The th term of a different number sequence is given by
Write down the first 3 terms of this sequence.
Yuen says there are no numbers that are in both of the sequences.
Yuen is correct.
Explain why.
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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?
If the sunflower grows at a faster rate, how would this affect your answer to part ()?
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Here are the first four terms of a sequence.
Find the nth term of this sequence.
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The th term of a sequence is
.
Write down an expression, in terms of and
, for the 3rd term.
The 3rd term of this sequence is 21 and the 6th term is 96.
Find the value of and the value of
You must show all your working.
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Here are the first five terms of an arithmetic sequence.
2 5 8 11 14
Write down an expression, in terms of , for the
th term of this sequence.
Is 299 a term of this sequence?
You must give a reason for your answer.
Write down an expression, in terms of , for the
th term of this sequence.
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Here are the first five terms of a sequence.
4 11 22 37 56
Find an expression, in terms of , for the
th term of this sequence.
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The th term of a sequence is given by
where
and
are integers.
The 2nd term of the sequence is —2
The 4th term of the sequence is 12
Find the 6th term of the sequence.
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Here are the first five terms of a different quadratic sequence.
0 2 6 12 20
Find an expression, in terms of , for the
th term of this sequence.
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Find the th term of each sequence.
4, 8, 12, 16, 20, .........
11, 20, 35, 56, 83, ..........
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is a geometric sequence.
Given that ,
and
are the first three terms of
, find the value of
.
You must show all your working.
Show that the th term of
is
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Louis and Robert are investigating the growth in the population of a type of bacteria.
They have two flasks A and B.
At the start of day 1, there are 1000 bacteria in flask A.
The population of bacteria grows exponentially at the rate of 50% per day.
Show that the population of bacteria in flask A at the start of each day forms a geometric progression.
The population of bacteria in flask A at the start of the 10th day is times the population of bacteria in flask A at the start of the 6th day.
Find the value of .
At the start of day 1 there are 1000 bacteria in flask B. The population of bacteria in flask B grows exponentially at the rate of 30% per day.
Sketch a graph to compare the size of the population of bacteria in flask A and in flask B.
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The table shows the first five terms of sequences A, B and C.
Sequence | 1st term | 2nd term | 3rd term | 4th term | 5th term | 6th term |
A | 3 | 4 | 5 | 6 | 7 |
|
B | 0 | 1 | 4 | 9 | 16 |
|
C | -3 | -3 | -1 | 3 | 9 |
|
Complete the table for the 6th term of each sequence.
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Write down the th term of sequence A.
i) Find the th term of sequence B.
[1]
ii) Find the value of when the
th term of sequence B is 8281.
[3]
i) Find the th term of sequence C in its simplest form.
[2]
ii) Find the 8th term of sequence C.
[1]
The th term of another sequence D is
.
Complete the table for the first four terms of sequence D.
Sequence | 1st term | 2nd term | 3rd term | 4th term |
D |
|
|
|
|
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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 1 2 3 5 8 13 ........ ........
Write down the first two terms of this sequence.
.......... ........... 3 11 14
i) Find the value of and the value of
.
2
10
[3]
ii) Find the value of , the value of
and the value of
.
-33
18
[5]
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The first two terms of a quadratic sequence are 10 and 17
Here is some information about the sequence.
Work out an expression for the nth term of the sequence.
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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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A sequence is defined using this term-to-term rule,
where and
are constants.
Given that ,
and
, find the value of
and the value of
.
= ................
= .................
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Here is a sequence.
3 | 15 |
Work out the next term.
Find the th term.
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A sequence is defined by the rule
If , calculate
i)
=............................[3]
ii)
=............................[3]
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