Question

The sum of the first 6 terms of an AP is 36 and that of the first 16 is 256. Find the sum of the first10terms

Answer 1

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

A/C to question ;

S6 = 6/2{ 2a + (6-1)d }
36 = 3(2a + 5d)
12 = 2a + 5d --------------(1)

again,
S16 = 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 10terms = 100