The common ratio of a G.P. is -frac{4}{5} and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The formula for the sum to infinity of a $G.P.$ is given by $S_{\infty} = \frac{a}{1-r}$,where $a$ is the first term and $r$ is the common ratio.G

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(B) The formula for the sum to infinity of a $G.P.$ is given by $S_{\infty} = \frac{a}{1-r}$,where $a$ is the first term and $r$ is the common ratio.Given,$r = -\frac{4}{5}$ and $S_{\infty} = \frac{80}{9}$.Substituting the values into the formula:$\frac{80}{9} = \frac{a}{1 - (-\frac{4}{5})}$$\frac{80}{9} = \frac{a}{1 + \frac{4}{5}}$$\frac{80}{9} = \frac{a}{\frac{9}{5}}$$a = \frac{80}{9} 	imes \frac{9}{5}$$a = 16$.Thus,the first term is $16$.

The common ratio of a $G.P.$ is $-\frac{4}{5}$ and the sum to infinity is $\frac{80}{9} .$ Find the first term.

Similar Questions

The ratio of the sums of the first $n$ even numbers and $n$ odd numbers is

If $a_1, a_2, ..., a_n$ are positive real numbers whose product is a fixed number $c$,then the minimum value of $a_1 + a_2 + ... + a_{n-1} + 2a_n$ is

The value of $\overline{0.037}$,where $\overline{0.037}$ stands for the number $0.037037037...$,is:

If $n$ geometric means are inserted between $a$ and $b$,then the $n^{th}$ geometric mean will be:

The sum of an infinite geometric series is $3$. $A$ series,which is formed by squares of its terms,has the sum also $3$. The first series is

Vedclass Test Series

Exam Paper Generator

Online Exam Module