Question

If the 13th term of an A.P is 21, then the sum of the first 25 terms is?

Answer 1

Answer:

As,we know that, the sum of n terms of an A.P. is given as

S

n

=

2

n

[2a+(n−1)d]

Therefore,

S

13

=

2

13

[2a+(13−1)d]

⇒21=13a+78d.....(1)

S

21

=

2

21

[2a+(21−1)d]

⇒13=21a+210d.....(2)

On solving (1)&(2), we get

a=

91

283

and d=

273

−68

Therefore,

S

34

=

2

34

[2×

91

283

+(34−1)(

273

−68

)]

⇒S

34

=17(

91

566

−

91

748

)

⇒S

34

=17(

91

566−748

)

⇒S

34

=17×(−

91

182

)=−34

Hence proved.

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