(i) Given a = 3, n = 8, S = 192, find d.
(ii) Given l = 28, S = 144 and there are total 9 terms. Find a.

Solutions:

(i) Provided that, 

The first term, a = 3,

The number of terms, n = 8

In addition, the sum of n words, S = 192

As we all know that,

S_n = n/2 [2a+(n -1)d]

192 = 8/2 [2×3+(8 -1)d]

192 = 4[6 +7d]

48 = 6+7d

42 = 7d

d = 6

(ii) Provided that, there are total of 9 terms and l = 28,S = 144.

Formula for sum of n terms,

S_n = n/2 (a + l)

144 = 9/2(a+28)

(16)×(2) = a+28

32 = a+28

a = 4