# The number of terms in an geometric progression

Hint : You can find the number of term in an arithmetic progression if you know the last term

Example

Find the number of terms for each of the following geometric progressions.
(a)$\frac{1}{4},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{6},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{9},\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}\frac{16}{729}$
(b)$15,5,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{5}{3},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{5}{9},\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}\frac{5}{729}$