we have -4,t, 3t +1 are terms of an A.P. what is t?

Given that -4, t, 3t+1 are terms in an arithmetical
progression.

Let us assume that the common difference
between terms is (r).

Then we know
that:

a1= -4

a2= a1+ r = -4 +
r = t

==> r - 4 =
t

==> t= r-4
 ....................(1)

Also, we know
that:

a3= a1+ 2r

==> -4
+ 2r = 3t+1

==> 2r = 3t + 5
.............(2)

Now we will substitute (1) into
(2).

==> 2r = 3t +
5

==> 2r = 3(r-4) +
5

==> 2r = 3r - 12 +
5

==> -r =
-7

==> r= 7

==>
t= r-4 = 7-4 = 3

==> t=
3.

Let us verify our
answer.

==> -4 , t , 3t+1  =  -4, 3,
10 are terms of an A.P where r = 7.