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

Question

Philoid · Accepted Answer

Let a and d be the first term and common difference, respectively of an AP

We know, Sum of first n terms of an AP

36 = 3[ 2a + 5d]

12 = 2a + 5d

2a = 12 - 5d [ eqn 1]

Now,

256 = 8[ 2a + 15d]

32 = 2a + 15d

32 = 12 - 5d + 15d [ using eqn 1]

20 = 10d

d = 2

using this value in eqn 1we get,

2a = 12 - 5(2)

2a = 2

a = 1

Now,

= 5(2 + 9(2))

= 5(20) = 100

So the sum of first 20 terms is 100