Tag: understanding geometric progressions

$\displaystyle { ar }^{ 4 }=48$
$\displaystyle { ar }^{ 8 }=768$
$\displaystyle \therefore \quad { r }^{ 4 }=16$
$\displaystyle \therefore \quad r=2$
$\displaystyle a.{ 2 }^{ 4 }=48$
or, $\displaystyle a=\frac { 48 }{ 16 } =3$
The GP is 3,6, 12,24,.....

A geometric series is a series for which the ratio of each two consecutive terms is a constant function of the summation index .

A geometric progression is a sequence of numbers where each term in the sequence is found by multiplying the previous term with a with a unchanging number called the common ratio.
Example: $2, 6, 18, 54, 108....$
This geometric sequence has a common ratio $3$.

$10, 20, 40, 80$ is an example of geometric sequence.
In geometric sequence, the ratio of succeeding term to the preceeding term is always equal.

A geometric series is the sum of the numbers in a geometric progression.

Geometric series is of the following form:

The sequence $6, 12, 24, 48....$ is a geometric progression as the ratio here is common.
The common ratio in the given series is $2$.

$1, 3, 9, 27, 81$ is a geometric sequence.
A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.