Question

sn=3n^2-2n. then find the AP

Answer 1

S1= 9-2
a =7

S2= 36-4
=32

so a2= 32-7=15

hence ap= 7,15,22,29.....

Answer 2

$S_n = 3{n}^{2} - 2n \\ \\ S_1 =3 \times {1}^{2} - 2 \times 1 = 3 - 2 = 1 \\ \\ a_1 =1 \\ \\ S_2 = 3 \times {2}^{2} - 2 \times 2=12 - 4 = 8\\ \\ a_2 = S_2 - S_1 = 8-1 = 7\\ \\ S_3 = 3 \times {3}^{2} - 2 \times 3=27 - 6 = 21\\ \\ a_3 = S_3 - S_2 = 21 - 8= 13\\ \\ \text{So the first three terms are: 1, 7, 13}\\ \\ \text{first \ term = 1}\\ \\ \text{common\ difference = 7-1 = 6}\\ \\ \textbf{A.P = 1, 7, 13, 19, 25...}$