Question

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

Answer 1

Recursive formula is `a_n=a_(n-1)xx1/5`

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 `50/250=10/50=2/10` are all `1/5`. Hence common ratio is `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)xx1/5`.