Question

The sum of 20 terms of an AP is 400 and that of 40 terms is 1600 Find the sum of first 10 terms and that of n terms?

Answer 1

Let first term be a

Constant be d

Then Sn=n2[2a+(n-1)d]

S20=10[2a+19d]

But S20=400

10[2a+19d]=400

2a+19d=40 eq.1

Also

S40=1600

20[2a+39d]=1600

2a+39d=80 eq.2

On solving eq.1 and eq2.

We get a=1,d=2

So S10=5[2×1+9×2]

S10=5×20

S10=100

Sn=n/2[2a+(n-1)d]

Sn=n/2[2+2n-2]

Sn=n/2×2n

Sn=n×n

Sn=n^2