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Question

If k, (2k1) and (2k+1) are the three successive terms of an AP, find the value of k.

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Solution

Given, k,(2k1) and (2k+1) are the three successive terms of an AP.
So, difference between two consecutive terms is same.
(2k1)k=(2k+1)(2k1)
2(2k1)=2k+1+k
4k2=3k+1
4k3k=1+2
or k=3
The value of k is 3.

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