Mathematics

A geometric progression multiplies by the same factor each time, so once you know the first term $a$ and common ratio $r$, you can write out all the terms. Here, you're given that the first three terms sum to 26 and $r=2$, so you can express the sum in terms of $a$ alone and solve. The key is recognizing that the second term is $ar$ and the third is $ar^2$—then it's just algebra.

A geometric progression multiplies by the same factor each time, so once you know the first term $a$ and common ratio $r$, you can write out all the terms. Here, you're given that the first three terms sum to 26 and $r=2$, so you can express the sum in terms of $a$ alone and solve. The key is recognizing that the second term is $ar$ and the third is $ar^2$—then it's just algebra.