Find x in a sequence of Arithmetic Progression (AP)

Question

If $(8x+1), (6x-1)$ and $(3x+5)$ are in an AP, find the value of $x$. This sum is from a question paper and there is no other information given. I was able to solve other sums which had more information available. But I'm stuck at this sum.

Answer 1

In an A.P, $$a_2-a_1=a_3-a_2$$ Here $a_1=8x+1, a_2=6x-1, a_3=3x+5$ So, $$(6x-1)-(8x+1) = (3x+5)-(6x-1)$$ $$\implies6x-1-8x-1=3x+5-6x+1$$ $$\implies-2x-2=-3x+6$$ $$\implies x=8$$ Therefore the value of $x$ is $8$

Hope it helps