The Geometric series formula or the geometric sequence formula gives the sum of a finite geometric sequence. The geometric series is that series formed when each term is multiplied by the previous term present in the series. The sequence will be of the form {a, ar, ar², ar³, …….}.

Geometric Series Formula

The geometric series formula is given by

Here a will be the first term and r is the common ratio for all the terms, n is the number of terms.

Solved Example Questions Based on Geometric Series

Let us see some examples on geometric series.

Question 1: Find the sum of geometric series if a = 3, r = 0.5 and n = 5.

Solution:

Given:

a = 3

r = 0.5

n = 5

s_n =

\begin{array}{l} \frac{a (1 - r^{n})}{1 - r} \end{array}

The sum of five terms is given by S₅=

\begin{array}{l} \frac{3 (1 - (0.5)^{5})}{1 - 0.5} \end{array}

= 5.8125

Question 2: Find S₁₀ if the series is 2, 40, 800,…..

Solution:

From the given,

a = 2

r = 20

n = 10

The 10th term in the series is given by S₁₀ =

\begin{array}{l} \frac{a (1 - r^{n})}{1 - r} = \frac{2 (1 - 20^{10})}{1 - 20} \end{array}

\begin{array}{l} \frac{2 (1 - 20^{10})}{1 - 20} = \frac{2 \times (- 1.024 \times 10^{13})}{- 19} \end{array}

\begin{array}{l} \frac{- 2.048 \times 10^{13}}{- 19} \end{array}

= 1.0778 × 10¹².

Geometric Series Formula

Solved Example Questions Based on Geometric Series

Comments

Leave a Comment Cancel reply