Question

The sum of n terms of three ap are S1 ,S2 ,S3 .the first term of each is unity and common difference are 1,2and3 respectively . Prove that S1 + S3 =2S2

Answer 1

Answer:

here sum of n terms of AP is Sn =n/2{2a+(n-1)d}

Step-by-step explanation:

S1=n/2{2+(n-1)1}=n(n+1)/2

{Where a=1,d=1}

S2=n/2{2+(n-1)2}=n/2(2n)=n^2

{Where a=1,d=2}

S3=n/2{2+(n-1)3}

=n/2n2+3n-3}={3n-1}

S1+S3=n^2+n+3n^2-n/2

=4n^2/2=2n^2=2S2

Hence proved that S1+S3=2S2