The sum of few terms of any ratio series is 7 | vedclass

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

Question

(a) $	herefore {n^{th}}$ term of series $ = a{r^{n - 1}}$$ = a\,{(3)^{n - 1}} = 486$ &hellip;..$(i)$

and sum of $n$ terms of series.

${S_n} = \

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(a) $	herefore {n^{th}}$ term of series $ = a{r^{n - 1}}$$ = a\,{(3)^{n - 1}} = 486$ &hellip;..$(i)$

and sum of $n$ terms of series.

${S_n} = \frac{{a({3^n} - 1)}}{{3 - 1}}$ &hellip;..$(ii)$

From $(i),$ $a\left( {\frac{{{3^n}}}{3}} ight) = 486$ or $a{.3^n} = 3 	imes 486 = 1458$

From $(ii),$ $a{.3^n} - a = 728 	imes 2$ or $a{.3^n} - a = 1456$

$1458 - a = 1456$

$&rArr;$  $a = 2$.

The sum of few terms of any ratio series is $728$, if common ratio is $3$ and last term is $486$, then first term of series will be

Similar Questions

If the sum of $n$ terms of a $G.P.$ is $255$ and ${n^{th}}$ terms is $128$ and common ratio is $2$, then first term will be

If in an infinite $G.P.$ first term is equal to the twice of the sum of the remaining terms, then its common ratio is

The sum of infinite terms of a $G.P.$ is $x$ and on squaring the each term of it, the sum will be $y$, then the common ratio of this series is

If $a,\,b,\,c$ are in $G.P.$, then

If the first term of a $G.P. a_1, a_2, a_3......$ is unity such that $4a_2 + 5a_3$ is least, then the common ratio of $G.P.$ is