Question

If 9+k,6+2k,23-k are in A.P then find k. ​

Answer 1

EXPLANATION.

• GIVEN

9 + k, 6 + 2k, 23 - k are in Ap

To find value of k

method = 1

in Ap common difference =

b - a = c - b

Therefore,

6 + 2k - ( 9 + k) = 23 - k - ( 6 + 2k )

6 + 2k - 9 - k = 23 - k - 6 - 2k

k - 3 = - 3k + 17

4k = 20

k = 5

method = 2

conditions of an Ap = 2b = a + c

2 ( 6 + 2k ) = 9 + k + ( 23 - k)

12 + 4k = 9 + k + 23 - k

12 + 4k = 32

4k = 20

k = 5

Therefore,

In both the conditions

value of k = 5