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Q.

The sum of the first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its first n terms from the choices given below.


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a

n 2  

b

(n+1) 2

c

n

d

(n + 1)

answer is D.

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Detailed Solution


It is given that the sum of the first 7 terms of an AP is 49 and the sum of its first 17 terms is 289.
We have to find the sum of its first n terms.
From the given information,
S 7 =49
We know that sum of n-terms in AP is,
S n = n 2 [2a+(n−1)d]
Substitute the known values in the formula,
7 2 (2a+6d)=49
a+3d=7                                                          ……(1)
Similarly, for the sum of the first 17 terms,
289= 17 2 [2a+16d]
a+8d= 289 17
a+8d=17                                                        ……(2)
Solve equations (1) and (2) by subtracting (1) from (2),
5d=10
d = 2
Substitute the value of d in equation (1),
a+3(2)=7 a=7−6 a=1
Then,
S n = n 2 [2×1+(n−1)×2]
=n[1+(n−1)]
S n = n 2
The sum of the first n terms is n 2 .
Hence, option 4 is correct.
 
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