Question

For what value of k will k+9,2k+7&5k+9 be the consecutive term of an AP

Answer 1

We know, in an A.P. there exists a common difference between consecutive terms.

So,

$(2k + 7) - (k + 9) = (5k + 9) - (2k + 7)$

$2(2k + 7) = (5k + 9) + (k + 9)$

$4k + 14 = 6k + 18$

$2k = - 4$

$k = - 2$

Answer 2

Hi ,

If a , b , c are in a.p then

2b = a + c

Here ,

a = k + 9 ,

b = 2k + 7,

c = 5k + 9,

Now ,

2b = a + c

2 (2k + 7 ) = k + 9 + 5k + 9

4k + 14 = 6k + 18

4k - 6k = 18 - 14

-2k = 4

k = 4/( -2 )

k = -2

I hope this helps you.

:)