Question

x - 1, x + 2 and 3x are the first three terms of an arithmetic sequence, find the first term and the fifth term by extracting the value of x.​

Answer 1

Since they're in arithmetic progression, the difference between consecutive terms is fixed.

`(x + 2) - (x - 1) = 3`

`3x - (x + 2) = 2x - 2 = 3 \implies 2x = 5 \implies x = \frac52`

Then the first term is

`x-1=\frac52 - 1 = \boxed{\frac32}`

and the fifth term is

`3x + 3 + 3 = 3\cdot\frac32 + 3 + 3 = \boxed{\frac21}2`