If x + 1, 2x - 1 and x + 5 are three consecutive terms of an AP, find the value of x

Question

Trying to solve but acquiring wrong answer

Answer 1

The first three terms of an AP are a, a+d, a+2d corresponding to x+1, 2x-1, x+5.

To find d we subtract the first and third terms so that x cancels out: 2d=x+5-(x+1)=4 so d=2.

To find a we use the second term: a+d=a+2=2x-1 so a=2x-3.

The AP is 2x-3, 2x-1, 2x+1 but these are equivalent to x+1, 2x-1, x+5.

So we can take any two matching terms: 2x-3=x+1, x=4; 2x+1=x+5, x=4. From this a=8-3=5.

The series is 5, 7, 9, ...