Find the number of ways in which $3$ distinct numbers can be selected from the set $\{3^1,3^2,\dots,3^{100},3^{101}\}$ so that they form gp..

My attempt.

I tried to take numbers like $3^1,3^3,3^5$ (whose powers have a common difference of $2$ then $3$ then $4$, and so on but that's lengthy..

2nd Attempt

we know for numbers to be in GP (geometrical progression)..

$b^2=ac$

we can write $b$ as some $3^k$, $a$ as $3^l$, and $c$ as $3^m$

We get the $2k=l+m$.

Now we have to find the triplets which are in ap(arithmetical progression) from the set $\{1,2,3,\dots,100,101\}$. How to do this.??