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.

Question

asked Sep 15, 2023 49.4k views

1 Answer

Gilonm · Answer 1 · 2023-09-22T08:38:29+0000

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

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