Question

Find the G.P; If the first term $a = 3$and the common ratio $r = 2.$

Answer 1

Hint: In the Geometric Progression, the ratio of any term to its preceding term is constant in a sequence of numbers. Geometric Progression is a sequence of numbers where each term is calculated by multiplying the previous one by a fixed, non-zero number called the common ratio.

Complete step-by-step answer:
To solve these types of problems,
The G.P. series is given by,
$ \Rightarrow a,ar,a{r^2},a{r^3},.....$
Given in the problem is to find G.P.
Given,
$a = 3$
$r = 2.$
Therefore the series is,
$ \Rightarrow 3,3 \times 2,3 \times {2^2},3 \times {2^3},.......$
$ \Rightarrow 3,6,12,24,........$
So, the correct answer is “3,6,12,24..”.

Note: $ \Rightarrow $If we multiply or divide a non-zero quantity to each term of the G.P, then the resulting sequence is also in G.P with the same common difference.
$ \Rightarrow $Reciprocal of all the terms in G.P also form a G.P.
$ \Rightarrow $ If all the terms in a G.P are raised to the same power, then the new series is also in G.P.
$ \Rightarrow $If${Y^2} = XZ$, then the three non-zero terms $X,Y,Z$are in G.P.