Question

Find the sum of first 30 terms of an AP whose 2 term is 2 and 7 term is 22​

Answer 1

Answer:

Let a be the first term d be the common difference of the given A.P.

Then, a

2

=2 and a

7

=22

⟹a+d=2 ............ (1)

and a+6d=22 .............. (2)

Solving these two equation, we get a=−2 and d=4.

∴S

30

=

2

30

{2×(−2)+(30−1)×4} ....[Puttingn=30,a=−2 andd=4inS

n

=

2

n

{2a+(n−1)d}]

⟹S

30

=15(−4+116)=15×112=1680

Hence, the sum of first 30 terms is 1680.