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.

–14, –13, –12, –11, ...

Answer 1

`a_(n)` = n - 15

Explanation:

there is a common difference between consecutive terms , that is

- 13 - (- 14) = - 12 - (- 13) = - 11 - (- 12) = 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 = - 14 and d = 1 , then

`a_(n)` = - 14 + 1 (n - 1 ) = - 14 + n - 1 = n - 15