Question

The sum of the first n terms of an arithmetic series is given by: Sn=5/2n^2 + 7/2n.

Determine: 3.2.1 The common difference.

3.2.2 The tenth term

Answer 1

the first term would be S1
= (5/2)(1) + (7/2)(1) = 6

the sum of the first 2 terms is S2
= (5/2)(4) + (7/2)(2) = 17

so the 2nd term = S2 - S1 = 17-6 = 11
which means the common difference must be 5

(just checking:
the first 4 terms would be : 6, 11, 16, 21
and the sum of the first 4 terms = 54
by your formula:
S4 = (5/2)(16) + (7/2)(4) = 54)

so term(10) = a+9d
= 6 + 9(5)
= 51

Answer 2

The first and last term of an A.p are -3 and 145 respectively.if the common difference is 4 .find 12th