2t+1, 12, 3t-2 are terms of A.P, find the value of t.

Given the terms (2t+1) , 12, (3t-2) are terms of an arithmetical
progression.

Let the common difference be r
.

Then we know that:

2t+1 = 12
-r

3t-2 = 12 +r

We will add both
equations.

==> 5t -1 =
24

==> 5t = 25

==> t=
5

To check the answer we will substitute into the
terms.

==> 2t+1 = 2*5+1 =
11

==> 12

==> 3t-2 =
3*5-2 = 15-2 = 13

==> 11, 12, 13, are terms of A.P and the
common difference is r= 1

Then the value of t =
5