Mathematics
For what value of k will 2k + 1, 3k + 3, and 5k − 1 be three consecutive terms of an A.P.?
1
2
4
6
AP
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Answer
We are given three consecutive terms of an A.P.:
2k + 1, 3k + 3, 5k − 1
In an arithmetic progression, the difference between consecutive terms is the same.
⇒ (3k + 3) - (2k + 1) = (5k - 1) - (3k + 3)
⇒ 3k + 3 - 2k - 1 = 5k - 1 - 3k - 3
⇒ k + 2 = 2k - 4
⇒ 2 + 4 = 2k - k
⇒ k = 6.
Hence, option 4 is the correct option.
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