Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

–8, –7, –6, –5,

Answer 1

`a_(n)` = n - 9

Explanation:

there is a common difference between consecutive terms, that is

- 7 - (- 8) = - 6 - (- 7) = - 5 - (- 6) = 1

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 = 1 , then

`a_(n)` = - 8 + 1 (n - 1) = - 8 + n - 1 = n - 9