Sequences

3 marks · Easy

Given the sequence 2, 5, 10, 17, 26, ... use the difference method to find the next two terms of the sequence.

(a)

Work out the first row of differences for the sequence.

[1 mark]

(b)

From your differences, find the next two terms of the sequence.

[2 marks]

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(a) 3, 5, 7, 9

(b) 37 and 50

Common mistakes: Carrying the pattern from incorrect differences

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Marking points

M1 (a) · 1 mark · Identifies correct first-row differences: 3, 5, 7, 9

M2 (b) · 1 mark · Finds next difference (11), adds to previous term (26+11=37) (follow-through)

A1 (b) · 1 mark · Finds second next difference (13), adds to previous (37+13=50) (follow-through)

Worked solution

Sequence: 2, 5, 10, 17, 26 First row of differences: 3 (5-2), 5 (10-5), 7 (17-10), 9 (26-17) Next difference: 11 (9+2) Next term: 26 + 11 = 37 Following difference: 13 (11+2) Next term: 37 + 13 = 50 Answers: 37, 50.