Answer:
[tex]g_n = 49+ 2n[/tex]
Step-by-step explanation:
Given
[tex]g_1=51[/tex]
[tex]g_n=g_{n-1}+2[/tex]
Required
Determine the explicit formula (missing from the question)
First, calculate g2
[tex]g_n=g_{n-1}+2[/tex]
[tex]g_2 = g_{2-1} +2[/tex]
[tex]g_2 = g_1 +2[/tex]
[tex]g_2 = 51 +2[/tex]
[tex]g_2 = 53[/tex]
So, we have:
[tex]g_1=51[/tex]
[tex]g_2 = 53[/tex]
Calculate the common difference:
[tex]d = g_2 - g_1[/tex]
[tex]d = 53 - 51[/tex]
[tex]d = 2[/tex]
The explicit formula is calculated using:
[tex]g_n = g_1 + (n-1)d[/tex]
This gives:
[tex]g_n = 51 + (n-1)*2[/tex]
[tex]g_n = 51 + 2n-2[/tex]
Collect Like Terms
[tex]g_n = 51 -2+ 2n[/tex]
[tex]g_n = 49+ 2n[/tex]
