# Geometric Sequence Calculator

The first number | |

common difference (r) | |

N^{th} term to obtain |

## Geometric Sequence

## a_{n} = a x r^{n-1} OR r x a ^{n-1}

In a sequence if the ratio between every two consecutive term is constant then the sequence is known as " Geometric Sequence ".

- nth term (a
_{n}) = a x r^{n-1}(or) a_{n}= r x a_{n-1} - Sum of the first n terms, S
_{n}= a x (r^{n}-1) / (r - 1) when r ≠ 1

and Sn = na when r = 1. - Sum of infinite terms, S
_{∞}= a / (1 - r) when |r| < 1 and S_{∞}diverges

when |r| ≥ 1.

Suppose, 'a ' is the first number and 'r' is the common ratio, then the sequence is of the form a, ar, ar^{2}, ar^{3}, ....,

Example:

Find a

Solution:

By the formula of geometric sequence,

Find a

_{15}of a geometric sequence if a_{13}= -8 and r = 1/3.Solution:

By the formula of geometric sequence,

a

a

Therefore, a

_{14}= r a_{13}= (1/3) (-8) = -8/3a

_{15}= r a_{14}= (1/3) (-8/3) = -8/9.Therefore, a

_{15}= -8/9.