Sequences

4 marks · Hard

The first term of an arithmetic sequence is 12. The common difference is 7. Calculate the sum of the first 30 terms of this sequence.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

3690 (±0)

Must show: Correct application of formula, Correct evaluation of the terms

Also accept:

Common mistakes: Using wrong formula (e.g. subtotal instead of full sum); Substituting n = 29

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Writes or identifies correct formula for the sum of the first terms: .

M2 · 1 mark · Correct substitution: , , into formula.

M3 · 1 mark · Calculates intermediary step, such as evaluating .

A1 · 1 mark · Final correct sum, 3690. (follow-through)

Worked solution

Given , , .

Correction: The sum is 3405, not 3690. (The previous value was a calculation error.)