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Question
k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is ______.
Options
–2
0
2
3
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Solution
k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is 2.
Explanation:
We know that, if a, b, c are in A.P.
Then 2b = a + c
Since k + 2, 2k + 7 and 4k + 12 are the first three terms of the given A.P.
∴ 2(2k + 7) = k + 2 + 4k + 12
`\implies` 4k + 14 = 5k + 14
`\implies` k = 0
∴ First term = k + 2
= 0 + 2
= 2
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