Question

In an AP 3rd term is 8 and the 9th term is 2 more than the 3 types of 3 Rd term then prove that the sum of 19 the term is 551

Answer 1

Answer...

3rd term=a+2d=8....(1)

9th term=a+8d

A.T.Q

a+8d=2+3(a+2d)

By solving,

a+8d=2+3a+6d

8d-6d+a-3a=2

-2a+2d=2

-a+d=1....(2)

From (1)...(2)

3d=9

d=3 and a=2

Now,sum of 19 terms is

n/2(2a+(n-1)d)

19/2(2×2+18×3)

19/2(58)

=19×29=551

Hence proved!!