Answer:
[tex]d = 6[/tex]
Step-by-step explanation:
Given
[tex]S_n = 3n^2 + 5n[/tex]
Required
Find d
First, find the sum of the first 1 term
[tex]S_1 = 3 * 1^2 + 5 * 1[/tex]
[tex]S_1 = 8[/tex]
The sum of the first 2 terms
[tex]S_2 = 3 * 2^2 + 5 * 2[/tex]
[tex]S_2 = 22[/tex]
Calculate the first term (a)
[tex]a = S_1[/tex]
[tex]a = 8[/tex]
Calculate the second term (T2)
[tex]T_2 = S_2 - S_1[/tex]
[tex]T_2 = 22 - 8[/tex]
[tex]T_2 = 14[/tex]
The common difference is:
[tex]d = T_2 - a[/tex]
[tex]d = 14 - 8[/tex]
[tex]d = 6[/tex]
