The sum of the first n term of ab arithmetic series is given by Sn=5/2n^2+7/2n

Question

Determine the first term and the common different and the tenth term

Answer 1

Sn = 5/2 n^2 + 7/2 n = n/2 (5n+7)
Sn = n/2 (2a+(n-1)d)

5(n-1)+5+7 = 5(n-1)+12
a=6 d=5

T10 = 12+9*5 = 57

check:
6 = 1/2 (12+0)
6+11 = 17 = 2/2 (12+5)
6+11+16 = 33 = 3/2 (12+10)
looking good.