91Ó°ÊÓ

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

For example, thesequence2, 6, 18, 54, ... is ageometric progressionwith common ratio 3.

The ration of 2^nd term and first term is called the common ratio.

The sequence:$32,\text{ â¶Ä‰}8\text{ â¶Ä‰},\text{ â¶Ä‰}2\text{ }\mathrm{.....}$

Each term in a geometric sequence can be expressed in terms of the first term $a_1$and the common ratio r. Since each succeeding term is formulated from one or more previous terms, this is a recursive formula.

First term $a_1=32$and the common ratio is:

$$\begin{gathered} r=\text{ â¶Ä‰}\frac{a_2}{a_1} \\ =\frac{8}{32} \\ =\frac{1}{4} \end{gathered}$$.

In order to calculate the next three terms of the geometric sequence substitute$n=4,5,6$ and 32 for$a_1$ into the formula $a_n=a_1{r}^{n−1}$.

Thus, next three terms of the sequence$32,\text{ â¶Ä‰}8\text{ â¶Ä‰},\text{ â¶Ä‰}2\text{ }\mathrm{.....}$are$\frac{1}{2},\text{ â¶Ä‰}\frac{1}{8},\text{ â¶Ä‰}\frac{1}{32}$.