Question

G1(1)=51
g(n)=g(n_1)+2

Answer 1

`g_n = 49+ 2n`

Explanation:

Given

`g_1=51`

`g_n=g_(n-1)+2`

Required

Determine the explicit formula (missing from the question)

First, calculate g2

`g_n=g_(n-1)+2`

`g_2 = g_(2-1) +2`

`g_2 = g_1 +2`

`g_2 = 51 +2`

`g_2 = 53`

So, we have:

`g_1=51`

`g_2 = 53`

Calculate the common difference:

`d = g_2 - g_1`

`d = 53 - 51`

`d = 2`

The explicit formula is calculated using:

`g_n = g_1 + (n-1)d`

This gives:

`g_n = 51 + (n-1)*2`

`g_n = 51 + 2n-2`

Collect Like Terms

`g_n = 51 -2+ 2n`

`g_n = 49+ 2n`