Question

if sn=an²+bn then prove that it is an Ap​

Answer 1

Answer:

This is easiest one

Step-by-step explanation:

Sn=an²+bn

prove it is AP

Sol.

Sum of n terms= an²+bn

S1=a1^1 +1b

=a+b

S2= a2²+2b

= 4a+2b

S3=a3²+3b

=9a+3b

Now,

first term is a+b = s1

sec. term= S2-S1

= 4a+2b-(a+b)

3a+b

third term= S3 - S1

=9a+3b-(4a+2b)

=5a+b

Now series,

a+b,3a+b,5a+b

if in ap

2b=a +c

2(3a+b)=a+b+5a+b

6a+2b=6a+2b