Question

# The ${{\text{n}}^{{\text{th}}}}$ term of a geometric progression is ${{\text{a}}_{\text{n}}}$= ${\text{a}}{{\text{r}}^{{\text{n - 1}}}}$, where r representsA. Common differenceB. Common ratioC. First termD. Radius

Given, ${{\text{n}}^{{\text{th}}}}$term of a geometric progression is ${{\text{a}}_{\text{n}}}$, and it is equal to ${\text{a}}{{\text{r}}^{{\text{n - 1}}}}$. We need to find what r represents.
The geometric progression is a progression of numbers with a constant ratio between each number and the one before. If the first term is k and the common ratio is m, then the geometric progression will be k, km, km$^2$, km$^3$,…, km$^{{\text{n - 1}}}$. Here , the nth term is km$^{{\text{n - 1}}}$. Comparing it with ${\text{a}}{{\text{r}}^{{\text{n - 1}}}}$, we get k = a and m = r i.e. a is the first term of the geometric progression and r is the common ratio.