Question

Let x-1, 2x+1 , x-7 are in ap. Find the value of x

Answer 1

In AP

2(2x+1)=(x-1)+(x-7)

4x+2=2x-8

2x=-10

x=-5

MARK BRAINLIEST.

FOLLOW.

Answer 2

   

$T_1=x-1 \\ \\ T_2=2x+1 \\ \\ T_3=x-7$

As they are in AP, the difference of two consecutive terms is constant, which means equal. I.e., common difference.

$\Rightarrow\ T_2-T_1=T_3-T_2$

$\Rightarrow\ (2x+1)-(x-1)=(x-7)-(2x+1) \\ \\ \Rightarrow\ 2x+1-x+1=x-7-2x-1 \\ \\ \Rightarrow\ x+2=-x-8 \\ \\ \Rightarrow\ x+x=-8-2 \\ \\ \Rightarrow\ 2x=-10 \\ \\ \Rightarrow\ x=\bold{-5}$

Thank you. :-))