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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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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The first 4 terms of a linear sequence are
      3    11   19    27
Circle the expression for the th term.
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Write an expression for theth term of the sequence below.
15Â Â Â 12Â Â Â 9Â Â Â 6
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A sequence is defined using this term-to-term rule.
If , findÂ
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Here is a sequence of numbers.
7,  5,  3,  1,  – 1, …
Find the next term in this sequence.
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These are the first five terms in a sequence.
Â
Find the next term.
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Here are the first 5 terms of an arithmetic sequence.
3 Â Â 9 Â Â 15 Â Â 21 Â Â 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 Â Â 10 Â Â 17 Â Â 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 Â Â 6 Â Â 10 Â Â 14 Â Â 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 Â Â 17 Â Â 23 Â Â 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 Â Â 10 Â Â 14 Â Â 18
Write an expression, in terms of , for the th term of this sequence.
The th term of a different arithmetic sequence isÂ
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 Â Â 9 Â Â 14 Â Â 19 Â Â 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 Â Â Â Â 2 Â Â Â Â 0 Â Â Â Â -4 Â Â Â Â -10
An expression for the th term of this sequence isÂ
Write down, in terms of , an expression for the th term of a sequence whose first five terms are Â
4 Â Â Â Â 4 Â Â Â Â 0 Â Â Â Â -8 Â Â Â Â -20
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The  th term of a number sequence is 2 + 1
Write down the first three terms of the 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 numbersÂ
The denominators of the fractions form the sequence of odd numbersÂ
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 an arithmetic sequence.
7 | 10 | 13 | 16 | 19 |
Find the sum of the first 100 terms of this sequence.
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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 .
Find an expression, in terms of , for the term of this sequence.
The term of a sequence is given byÂ
There are numbers that are terms in both the sequence and the sequenceÂ
Find one of these numbers.
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Here are the first five terms of a number sequence.
7 Â Â Â 11 Â Â Â 15 Â Â Â 19 Â Â Â 23
Find an expression, in terms of , for the th term of this sequence.
The th term of a different number sequence is given byÂ
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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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.
2Â Â 5Â Â 8Â Â 11Â Â 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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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.
  Â
1 Â Â Â 2Â Â Â Â 3 Â Â Â 5 Â Â Â 8Â Â Â Â 13Â Â Â Â Â ........... Â Â Â Â ...........
Write down the first two terms of this sequence.
.............     .............  3   11   14
      2       10
[3]
      -33            18
[5]
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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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The sum of the first terms of an arithmetic series, , is 292
The 2nd term of is 8.5
The 5th term of is 13
Find the value of .
Show clear algebraic working.
......................................................Â
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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 byÂ
Mario will save a total of $33 125 from 2021 to 2070
Work out the value of .
....................
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The first term of an arithmetic series is –6
The sum of the first 30 terms of is 2865
Find the 9th term of .
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In an arithmetic series, the term isÂ
In the same arithmetic series, the term isÂ
Work out the sum of the first terms of the arithmetic series.
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Work out the sum of the multiples of between andÂ
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Here are the first five terms of an arithmetic sequence.
Work out the sum of all the terms from the term to the term inclusive.
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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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A sequence is defined by the ruleÂ
If , calculate
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An arithmetic series has first term and common difference .
The sum of the first terms of the series is four times the sum of the first terms of the series.
Find an expression for a in terms of .
Show your working clearly.
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The nth term of an arithmetic series is  where for all
The sum to terms of the series is
Given that and thatÂ
find the value of
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Here are the first four terms of an arithmetic series.
         Â
Given that the 15th term of the series is ,
calculate the sum of the first 30 terms of the series.
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and are three consecutive terms of an arithmetic sequence.
Prove that the common difference of the sequence isÂ
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An arithmetic series has first term and common difference , where is a prime number.
The sum of the first n terms of the series is and
Find the value of and the value of
Show clear algebraic working.
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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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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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The term of an arithmetic series, , isÂ
The sum of the first terms of isÂ
Find the term of .
Show your working clearly.
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The 3rd term of an arithmetic series, , is 19
The sum of the first 10 terms of is 290
Find the 10th term of .
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