Sequences

4 marks · Normal

The 4th term of an arithmetic sequence is 15 and the common difference is 6.

(a)

Find the first term of the sequence.

[2 marks]

(b)

Calculate the 10th term of the sequence.

[2 marks]

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

(a) -3

(b) 51

Common mistakes: Miscounting n−1 vs n

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Use formula for nth term: a+(n−1)d = 15 for n = 4.

A1 (a) · 1 mark · Correct calculation and deduction of first term: −3.

M2 (b) · 1 mark · Use nth term = first term + (n−1)d for n = 10. (follow-through)

A2 (b) · 1 mark · Correct value for the 10th term: 51. (follow-through)

Worked solution

Let the first term be a. The nth term of an arithmetic sequence is a + (n − 1)d. We know:

For the 10th term: