Question

Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.

Answer 1

Answer:

$a_n = -11-14n$

Step-by-step explanation:

Given

$a_1 = -25$

$a_n = a_{n-1}-14$

Required

The explicit formula

First, calculate $a_2$

Set n=2; So:

$a_2 = a_{2-1}-14$

$a_2 = a_{1}-14$

Substitute -25 for $a_1$

$a_2 = -25-14$

$a_2 = -39$

Calculate the common difference (d)

$d = a_2 - a_1$

$d = -39 --25$

$d = -14$

So, the nth term is:

$a_n = a_1 + (n - 1)d$

$a_n = -25+ (n - 1)*-14$

Open bracket

$a_n = -25-14n + 14$

Collect like terms

$a_n = 14-25-14n$

$a_n = -11-14n$