Geometric Progression.

Assume any GP, then using the relation given find the value of common ratio.
Plug-in common ratio in the information given about sum of first two terms and find first term.
Now we have everything what is needed to find out the sum of an infinite G.P. .
Plug-in those values and calculate.

A. 16

Let the terms of GP be
a,ar,ar²…..
with “a” being the first term and “r” being the common ratio.

It is given that,
Each term =3*(Sum of all the terms that follow)

Let’s take the first term,
So
a=3*(ar+ar²+ar³+…..)
a=3*ar(1+r+r²+…..)
1=3r*1/(1-(r)) {Sum of infinite GP =first term /(1-common ratio ) when |r|<0}

Solving, r=1/4

Now the sum of first two terms is 15,
So
a+ar=15
a(1+r)=15
a(1+(1/4))=15
On solving, a=12

Now we have to find the sum of this GP when added to infinity.
We know that the sum of an infinite GP=a/(1-r)
Plug-in the values now ,
Sum=a/(1-r)
=12/(1-(1/4))
=16