Name: Geometric Progression
Uploaded: 2019-07-19
Duration: 6 min 13 s
Description: A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number. Learn more about GP and...

Question

Find the geometric progression whose

4^{th}

term is

54

and

7^{th}

term is

1458

.

Accepted Answer

Given, $4^{th}$ term of a geometric progression is $54$ and the $7^{th}$ term is $1458$ .

$n^{th}$ term of a geometric progression, $T_{n} = a r^{n - 1}$ , where $a$ is the first term and $r$ is the common ratio

$∴ a r^{4 - 1} = 54$

$\Rightarrow a r^{3} = 54$ _______ $(1)$

And $a r^{7 - 1} = 1458$

$\Rightarrow a r^{6} = 1458$ ______ $(2)$

Dividing equation $(2)$ by equation $(1)$ , we get,

$\frac{a r^{6}}{a r^{3}} = \frac{1458}{54}$

$\Rightarrow r^{3} = 27$

$\Rightarrow r^{3} = 3^{3}$

$\Rightarrow r = 3$

Substituting $r = 3$ in equation $(1)$ , we get,

$a \times 3^{3} = 54$

$\Rightarrow a = \frac{54}{27}$

$\Rightarrow a = 2$

$∴ a = 2, r = 3$

Hence, the geometric progression is $2, 6, 18, 54, \dots . . .$ .

Find the geometric progression whose $4^{th}$ term is $54$ and $7^{th}$ term is $1458$ .

Important Questions on Arithmetic and Geometric Progressions

Learn and Prepare for any exam you want !

Find the geometric progression whose 4th term is 54 and 7th term is 1458.

Important Questions on Arithmetic and Geometric Progressions

Learn and Prepare for any exam you want !

Find the geometric progression whose $4^{th}$ term is $54$ and $7^{th}$ term is $1458$ .