Question

If the sum of the first 6 terms of an AP is 36 and that of the first 16 terms is 256,find the sum of the first 10 terms.

Answer 1

Answer :

100

Solution :

Sum of n terms = n/2{2a + (n -1)d}

According to question,

S_6 = 6/2{2a + (6-1)d}

36 = 3(2a + 5d)

12 = 2a + 5d ----------- (1)

again,

S_16 = 16/2{2a + (16-1)d}

256 = 8{2a + 15d}

32 = 2a + 15d ---------- (2)

solve eqns (1) and (2)

10d = 20

d = 2 put in equation (1)

a = 1

now,

sum of 10th terms = S10 = 10/2{2a +(10-1)d}

= 5{2 × 1 + 9 ×2}

= 5 {2 + 18}

= 100

Hence, sum of first 10 terms = 100