R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 3: EXERCISE 20.3

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

How many terms of the sequence $\sqrt{3},3,3\sqrt{3},\dots$ must be taken to make the sum $39+13\sqrt{3}$?

The sum of n terms of the G.P. $3, 6, 12,...$ is $381$. Find the value of $n$.

The common ratio of a $\mathrm{G}.\mathrm{P}.$ is $3$ and the last term is $486$. If the sum of these terms be $728$, find the first term.

The ratio of the sum of first three terms is to that of first $6$ terms of a $\mathrm{G}.\mathrm{P}.$ is $125:152$. Find the common ratio.

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

A person has $2$ parents, $4$ grandparents, $8$ great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his own.

A $\mathrm{G}.\mathrm{P}.$ 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 $\mathrm{G}.\mathrm{P}.$.