# What is the recursive formula for geometric sequence {2,10,50,250,..........}?

Jan 30, 2017

Recursive formula is ${a}_{n} = {a}_{n - 1} \times \frac{1}{5}$

#### Explanation:

In a Geometric sequence, the ratio of each term to its preceding term is always constant and is known as common ratio $r$. Here, we observe that the ratios $\frac{50}{250} = \frac{10}{50} = \frac{2}{10}$ are all $\frac{1}{5}$. Hence common ratio is $\frac{1}{5}$.

Recursive formula is the formula, which generates subsequent term from its preceding term.

For example ${a}_{n}$ as a function of ${a}_{n - 1}$.

It is apparent that in the given Geometric sequence recursive formula is ${a}_{n} = {a}_{n - 1} \times \frac{1}{5}$.