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

Answer 1

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