If third term of a G.P. is 4 then product of its first 5 terms is

English

Gujarati

Hindi

8. Sequences and Series

easy

If the third term of a $G.P.$ is $4$ then the product of its first $5$ terms is

A

${4^3}$

B

${4^4}$

C

${4^5}$

D

None of these

(IIT-1982)

Solution

(c) Given that $a{r^2} = 4$

Then product of first $5$ terms

$ = a(ar)(a{r^2})(a{r^3})(a{r^4}) = {a^5}{r^{10}} = {[a{r^2}]^5} = {4^5}$.

Standard 11

Mathematics

Share

Similar Questions

Let $\mathrm{a}$ and $\mathrm{b}$ be be two distinct positive real numbers. Let $11^{\text {th }}$ term of a $GP$, whose first term is $a$ and third term is $b$, is equal to $p^{\text {th }}$ term of another $GP$, whose first term is $a$ and fifth term is $b$. Then $\mathrm{p}$ is equal to

hard

(JEE MAIN-2024)

If the sum of three terms of $G.P.$ is $19$ and product is $216$, then the common ratio of the series is

easy

How many terms of the $G.P.$ $3, \frac{3}{2}, \frac{3}{4}, \ldots$ are needed to give the sum $\frac{3069}{512} ?$

medium

If $b$ is the first term of an infinite $G.P$ whose sum is five, then $b$ lies in the interval

hard

(JEE MAIN-2018)

The sum of the first five terms of the series $3 + 4\frac{1}{2} + 6\frac{3}{4} + ……$ will be

easy