Find the sum of the first 4 terms of a geometric progression if a3 = 1 and the common ratio between consecutive terms is 1/2.

Let the terms of a geometric progression be
:

a1, a2, a3, a4

Given that
a3= 1 and the common difference is 1/2.

==> Then we
know that:

a3 = a1*r^2

1 = a1*
(1/2)^2

1= a1/ 4

==>
a1= 4

==> a2= a1*r = 4* 1/2 =
2

==> a3= a1*r^2 = 4*1/4 =
1

==> a4= a1*r^3 = 4*(1/8) =
1/2

Then the terms are:

4, 2,
1, 1/2

We will find the
sum.

==> S = 4 + 2 + 1 + 1/2 =
7.5

Then the sum of the first 4 terms is
7.5