Question

The first two terms of an arithmetic sequence are x+2 and 3x-2 and the sixth term is 5x. Find the value of x

Answer 1

Okay, the first term is x+2, then an arithmetic sequence steps up by some increment each term.

Think of our sequence like this:
x+2, x+2+y, x+2+2y , x+2+3y, x+2+4y, x+2+5y

But we know that the second term is equal to 3x-2. That means we can solve for y:
3x-2 = x+2+y