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.

–4, –3, –2, –1, ...

Answer 1

`a_(n)` = n - 5

Explanation:

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

- 3 - (- 4) = - 2 - (- 3) = - 1 - (- 2) = 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 = - 4 and d = 1 , then

`a_(n)` = - 4 + 1 (n - 1) = - 4 + n - 1 = n - 5