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# If  the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P. - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Question

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

#### Solution

Let the first term and the common difference of the given AP be a and d, respectively.

Sum of the first 7 terms, S7 = 49

We know

S=n/2[2a+(n-1)d]

=>7/2(2a+6d)= 49

=>7/2xx2(a+3d)=49

⇒ a+3d=7             .....(1)

Sum of the first 17 terms, S17 = 289

=>17/2(2a+16d)=289

=>17/2xx2(a+8d)=289

=>a+8d=289/17=17

⇒ a+8d=17           .....(2)

Subtracting (2) from (1), we get

5d=10

⇒ 2

Substituting the value of d in (1), we get

a = 1

Now,

Sum of the first n terms is given by

S_n=n/2[2a+(n-1)d]

=n/2[2xx1+2(n-1)]

= n(1+n-1)=n^2

Therefore, the sum of the first n terms of the AP is n2.

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Solution If  the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P. Concept: Sum of First n Terms of an AP.
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