Edexcel IGCSE Math A 3.1.HA arithmetic sequence proof

Practise the arithmetic-proof question by subtracting consecutive algebraic terms, simplifying both differences and showing they match.

Exam points

Subtract consecutive algebraic terms to form expressions for the common difference.
Simplify both differences and prove the given terms form an arithmetic sequence.

[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.

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3.1.HA First term and common difference question 1