IXL - Find the value of an infinite geometric series (Precalculus practice)

Find the sum of the infinite geometric series.

Write your answer as an integer or a fraction in simplest form.

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Find the sum of the infinite geometric series.

Write your answer as an integer or a fraction in simplest form.

A sequence is an ordered list of numbers. This list can have a finite number of terms or infinitely many terms.

A series is the sum of a sequence. The infinite series

is geometric if the ratios of consecutive terms are all defined and equal to the same number

(the common ratio of the series).

the series

converges,

which means it equals a number. The sum of the series is:

–

To find the sum, find the common ratio

and the initial term of the series.

Find the common ratio

Take the ratio of the first two terms.

Since the series is geometric, the ratio between any two consecutive terms is

Find the initial term.

The first term in the series is 5, so the initial term is

Find the sum.

Plug

and

into the formula for the sum of an infinite geometric series.

–

The sum of the series is 15.

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