Question

Write the explicit formula for the sequence shown below
3, -3, -9, -15

Answer 1

`a_(n)` = 9 - 6n

Explanation:

There is a common difference d between consecutive terms, that is

d = - 3 - 3 = - 9 - (- 3) = - 15 - (- 9) = - 6

This indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = - 6 , thus

`a_(n)` = 3 - 6(n - 1) = 3 - 6n + 6 = 9 - 6n