CAIE IGCSE Mathematics E2.7 Sequences Question Bank

Practise finding nth-term formulae for geometric sequences by identifying the common ratio and matching the first listed term.

Exam points

[Maximum number: 4]

(a)

Find the nth term of each sequence.

[ 4 ]

(i)

$6, \quad 13, \quad 32, \quad 69, \quad 130, \quad \ldots$

[ 2 ]

$n^{3}+5$ oe final answer

2

B1 for any cubic
or common third differences of 6
(at least 2)
or for correct answer seen and spoilt

(ii)

$100, \quad 50, \quad 25, \quad 12.5, \quad 6.25, \quad \ldots$

[ 2 ]

$100\times2^{1-n}$ oe final answer
B1 for $2^{-n+k}$ oe or $(\frac12)^{n+k}$ oe in answer, or for correct answer seen and spoilt

[Maximum number: 2]

These are the first five terms of a different sequence.
1, 3, 9, 27, 81
Find the nth term of this sequence.

$3^{n-1}$
B1 for $3^{an+k},\ a\ne0$ , or $3^c$ for any integer c>1

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