Question

Consider a sequence given by the formula an = an−1 − 5, where a1 = 12 and n ≥ 2.

Answer 1

Answer:

$a_{n} = 12 + (n - 1) (-5)$

Step-by-step explanation:

An explicit formula has two parts in it.

1) The initial value i.e. $a_{1} = 12$

2) The common difference between consecutive terms

To find the common difference we will use the first 5 terms which are as follow

12, 7, 2, -3, -8

the common difference is of -5

The general formula for an explicit arithmetic equation is as follow

$a_{n} = a_{1} + (n-1) d$

(This is an arithmetic sequence since it has a common difference)

Where

$a_{1}$ is the initial value

$n$ is the nth term

$d$ is the common difference

hence the explicit formula becomes

$a_{n} = 12 + (n - 1) (-5)$