Question

Find the value of k if 8k + 4 = 6k - 2 = 2 k - 7 are three consecutive terms of an AP.

Answer 1

let the consecutive three terms of the AP be a, a+d and a + 2d

a = 8k+4 ----------------eq... 1

a+d = 6 k -2-------------eq... 2

a+2d = 2k-7------------eq... 3

eqn 2 - eqn 1

a+d -a = 6k-2 -(8k+4) = 6k-2-8k-4

d = -2k -6 --------------eq... 4

Now

a+d +d = a+ 2d

or eqn 2+eqn 4 = eqn 3

6 k -2 + (-2k-6) = 2k-7
6k-2-2k-6 = 2k-7
4k-8 = 2k-7
4k-2k = 8-7
2k = 1
k = 1/2

there fore the tree terms of the AP are

8k+4 =8*1/2 +4 = 4+4 = 8

6k-2 = 6*1/2-2 = 3-2 = 1

and 2k-7 = 2*1/2 - 7 = 1-7 = -6