Question

Find the first term and the common difference of an AP in which the sum of the first 11terms is 352and the sum of the next 10 terms is 845.

Answer 1

Answer:

Let a be the first term and d be the common difference

Now,

S1=n2[2a+(n-1)d]

S2=2n2[2a+(2n-1)d]

S3=3n2[2a+(3n-1)d]

Now, 3(S2-S1)

=3[2n2(2a+(2n-1)d)-n2(2a+(n-1)d)]

=3[n2(2(2a)-2a)+n2(2(2n-1)d-(n-1)d)]

=3[n2(2a)+n2(4n-2-n+1)d)]

=3[n2(2a)+n2(3n-1)d)]

=3n2[2a+(3n-1)d]

=S3 (Proved)