Question

2 These are the first four terms of a sequence. Find the nth term of this sequence. 15 7 -1 -9​

Answer 1

`a_(n)` = - 8n + 23

Explanation:

there is a common difference between consecutive terms in the sequence, that is

7 - 15 = - 8

- 1 - 7 = - 8

- 9 - (- 1) = - 9 + 1 = - 8

This indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + d(n - 1)

a₁ is the first term, d the common difference , n the term number

here a₁ = 15 and d = - 8 , then

`a_(n)` = 15 - 8(n - 1 ) = 15 - 8n + 8 = - 8n + 23