R S Aggarwal Solutions for Exercise 3: EXERCISE 12C

Find the sum of the GP:

$1+3+9+27+\dots$ to $7$ terms

Find the sum of the GP:

 $1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\dots$ to $9$ terms

Find the sum of the geometric series $3+6+12+\dots +1536$

How many terms of the series $2+6+18+\dots .$ must be taken to make the sum equal to $728 ?$

The common ratio of a finite GP is $3$ and its last term is $486$. If the sum of these terms is $728,$ find the first term.

The $4^{th}$ and $7^{th}$ terms of a GP are $\frac{1}{27}$ and $\frac{1}{729}$ respectively. Find the sum of $n$ terms of the GP.

A GP consists of an even number of terms. If the sum of all the terms is $5$ times the sum of the terms occupying the odd places, find the common ratio of the GP.

Show that the ratio of the sum of first $n$ terms of a GP to the sum of the terms from $(n+1{)}^{th}$ to ${\left(2n\right)}^{th}$ term is $\frac{1}{r^n}$