Question

​ g(1)=−19 g(n)=g(n−1)+6 ​ Find an explicit formula for g(n)g(n)g, left parenthesis, n, right parenthesis. g(n)=g(n)=g, left parenthesis, n, right parenthesis, equals

Answer 1

Answer:

$g(n) = 6n -25$

Step-by-step explanation:

Given:

$g(1) = -19$

$g(n) = g(n - 1) + 6$

Required

The explicit formula

Let n = 2; So, we have:

$g(n) = g(n - 1) + 6$

$g(2) = g(2 - 1) + 6$

$g(2) = g(1) + 6$

$g(2) = -19 + 6$

$g(2) = -13$

So, we have:

$g(1) = -19$ ----- First term

$g(2) = -13$

Calculate common difference (d)

$d = g(2) - g(1)$

$d = -13 --19$

$d = 6$

The explicit function is then calculated as:

$g(n) = a + (n - 1)d$

Where

$a = -19$ --- First term

So:

$g(n) = a + (n - 1)d$

$g(n) = -19 + (n - 1)*6$

Open bracket

$g(n) = -19 + 6n - 6$

Collect like terms

$g(n) = 6n - 6-19$

$g(n) = 6n -25$