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

Answer:

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 \(a_{n}=a_{n-1} \times \frac{1}{5}\).