Edexcel IGCSE Math A 3.1 Sequences Question Bank

Practise sequence work from pattern continuation to nth terms, arithmetic proofs and series sums involving unknown constants.

Exam points

find terms from nth-term formulae, term-to-term rules or drawn patterns
prove arithmetic behaviour by comparing consecutive algebraic terms
use arithmetic series formulae to solve for a, d or the number of terms

Covered syllabus points

3.1.A Generating sequences 3.1.B Subsequent terms of an integer sequence and the rule 3.1.C nth terms of arithmetic sequences 3.1.HA First term and common difference 3.1.HB nth-term formula for arithmetic sequences 3.1.HC The sum of the first n terms of an arithmetic series

[Maximum number: 3]

Here are the first four terms of an arithmetic sequence.

$1\qquad4\qquad7\qquad10$

(a)

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

[ 2 ]

3n-2

M1 for 3n+k, where $k\ne -2$ , or equivalent.
A1 for 3n-2, or equivalent such as 1+(n-1)3.
Working not required, so a correct answer scores full marks unless from obvious incorrect working.

(b)

The nth term of a different arithmetic sequence is 5n+17.

Find the 12th term of this sequence.

[ 1 ]

[Maximum number: 4]

21(2 x+23),(8 x+2) and ( 20 x-52 ) are three consecutive terms of an arithmetic sequence.
Prove that the common difference of the sequence is 12

Common differences:
(8x+2)-(2x+23)=6x-21(20x-52)-(8x+2)=12x-54
Equate:
6x-21=12x-54x=5.5
Then:
$8(5.5)+2=46,\qquad 20(5.5)-52=58$
so the common difference is:
58-46=12.
Required result shown.

[Maximum number: 5]

The first term of an arithmetic series is 10
The 20 th term of the series is 86
The sum of the first N terms of the series is 5194
Work out the value of N
Show your working clearly.

Twentieth term:
$86=10+19d\quad\Rightarrow\quad d=4$
Sum:
$5194=\frac{N}{2}\left(2(10)+(N-1)4\right)$ $5194=\frac{N}{2}(4N+16)$ $N^2+4N-2597=0$ (N-49)(N+53)=0

Final answer:
N=49

M1 for finding d=4. M1 for correct substitution into the sum formula. M1 for a correct quadratic. M1 for solving. A1 cao.

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Covered syllabus points

3.1 Sequences question 1

Question (a)

Question (b)

3.1 Sequences question 2

3.1 Sequences question 3