Question

An=an−1−4 a1=15 to explicit formula

Answer 1

`a_n=3n-12`

Explanation:

We are given the recursive formula:

`a_n=a_(n-1)-4, a_1=15`

This is the recursive formula for an arithmetic sequence.

The explicit formula for an arithmetic sequence is given by:

`a_n=a_1 + d({n-1} )`

Where d=3 is the common difference.

We plug in this values to get:

`a_n=15 + 3({n-1} )`

We now expand and simplify to get:

`a_n=15 + 3n-3`

We simplify to obtain:

`a_n= 3n-12`