Question

What is the value of x if x-1,x+2,2x-1,......is an AP

Answer 1

The value of x in the given arithmetic sequence x-1,x+2,2x-1,... is 6

Step-by-step explanation:

Given that x-1,x+2,2x-1,... is an arithmetic sequence

To find the value of x in the given arithmetic sequence :

First put x=6 in the sequence x-1,x+2,2x-1,... we get

6-1,6+2,2(6)-1,...

5,8,11,...

Now verify that 5,8,11,... is an arithmetic sequence

Let $a_1=5$ ,$a_2=8$ ,$a_3=11$,...

To find the common difference d

$d=a_2-a_1$

SUbstituting the values we get

d=8-5

Therefore d=3

$d=a_3-a_2$

Substituting the values we get

d=11-8

Therefore d=3

Therefore the common difference d is 3

Therefore the sequence 5,8,11,... is an arithmetic sequence

Hence the value of x in the given arithmetic sequence x-1,x+2,2x-1,... is 6