SUM OF AP 1

The sum of first 20 terms of an AP is 1380, and the last term is 97. Find the 1^st term. 

Solution

A₁ = ?, n=20, A_n = 97, S_n =1380

S_n = n(A₁ + A_n)

       2

1380 = 20(A₁ + 97)

             2

1380 = 10(A₁ + 97)

1380 = 10A₁ + 970

1380 - 970= 10A₁

410= 10A₁

410= 10A₁

10     10

41= A₁

Hence 1^st term is 41.

TRYTHIS……………

The sum of first 30 terms of an AP is 2475, and the last term is 105. Find the 1^st term.