CAT 2025 Slot 2 — QA Question 8

Let $a _ { n }$ be the $n ^ { \text {th } }$ term of a decreasing infinite geometric progression. If $a _ { 1 } + a _ { 2 } + a _ { 3 } = 52$ and $a _ { 1 } a _ { 2 } + a _ { 2 } a _ { 3 } + a _ { 3 } a _ { 1 } = 624$, then the sum of this geometric progression is