Here's a simple javascript solution. We basically have two hashmaps - prev and next to keep track of items we've visited and ones that we still need to visit. Each time we find a geomatric set, we compute the sum based on the number of repeating characters and add it to the total counter. I derived the solution from the following youtube explanation.

https://www.youtube.com/watch?v=7YKr0ELmam4

function countTriplets(arr, r) { if(arr.length < 3) { return 0; } const prev = {}; const next = {}; for(let x of arr){ if(!next[x]) { next[x] = 1;
} else { next[x]++; } }

let current = null;
let counter = 0;
//a/r, a, a*r
for(let i = 0; i < arr.length; i++) {
    current = arr[i];
    const left = current/r;
    const right = current * r;
    next[current]--;
    let sum = 1;
    if(prev[left] && next[right]) {
        sum *= prev[left] 
        sum *= next[right]
        counter += sum;
    }
    if(!prev[current]) {
        prev[current] = 1;
    } else {
        prev[current]++;
    }
}
return counter;

}