Question

Write down in terms of n, an expression for the nth term

of the following sequence
-8 -15 -22 -29 -36

Answer 1

`a_(n)` = - 7n - 1

Explanation:

There is a common difference between consecutive terms , that is

- 15 - (- 8) = - 22 - (- 15) = - 29 - (- 22) = - 36 - (- 29) = - 7

This indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 8 and d = - 7 , then

`a_(n)` = - 8 - 7(n - 1) = - 8 - 7n + 7 = - 7n - 1