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Question

 If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 then find the common difference of the AP.


Your Answer
A
1
Correct Answer
B
2
Your Answer
C
3
Your Answer
D
10

Solution

The correct option is A 2
Let, 'a' be the first term and 'd' be the common difference of the AP.
Sum of n terms of an AP is:
n2×(2a + (n-1)d)
Sum of first 7 terms
               = 72×(2a + (7-1)d)
           = 72× (2a + 6d)
       = 7 × (a+3d)
and Sum of first 17 terms
        = 172×(2a + (17-1)d)
    = 172× (2a + 16d)
 = 17 × (a + 8d)
Given, Sum of first 7 terms = 49 and Sum of first 17 terms = 289
 7 × (a+3d) = 49  
a + 3d = 7 ......(1)
and, 17 × (a + 8d) = 289
a + 8d = 17.........(2)
Subtracting (1) from (2), we get
5d = 10
d = 2
Common difference of the given AP is 2.

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