Question

If 3 k - 2, 4k - 6 and k + 2 are three consecutive term of AP then find the value of k.​

Answer 1

Given :

3k-2 , 4k-6 and k+2 are three consecutive terms of AP.

To find :

Value of k

Solution :

As the given terms are in AP,

The difference between second term and first term is equal to difference between third term and second term also known as common difference.

d = second term - first term

{ Here d is called Common diffence }

d = (4k-6) - (3k-2)

d = 4k - 6 - 3k + 2

d = k - 4 equation 1

Also,

d = third term - second term

d = (k+2) - (4k-6)

d = k+2 - 4k + 6

d = -3k + 8

Put value of d from equation 1 into above equation.

k - 4 = -3k + 8

k + 3k = 8 + 4

4k = 12

k = 12÷4

k = 3

ANSWER :

k = 3