G Tewani Solutions for Chapter: Progression and Series, Exercise 2: DPP

If $a_1, a_2, a_3,\dots$ are in $\mathrm{G}.\mathrm{P}.,$ where $a_i\in C$ (where $C$ stands for set of complex numbers) having $r$ as common ratio such that $\sum _{k=1}^n{a}_{2k-1}=\sum _{k=1}^n{a}_{2k+3}\ne 0$, then the number of possible values of $r$ is

If $a, b, c$ are real numbers forming an $\mathrm{A}.\mathrm{P}.$ and $3+a, 2+b, 3+c$, are in $\mathrm{G}.\mathrm{P}.,$ then minimum value of $ac$ is

$a, b, c, d$ are in increasing $\mathrm{G}.\mathrm{P}.$, if the $\mathrm{A}.\mathrm{M}.$ between $a$ and $b$ is $6$ and the $\mathrm{A}.\mathrm{M}.$ between $c$ and $d$ is $54$, then the $\mathrm{A}.\mathrm{M}.$ of $a$ and $d$ is

The numbers $a, b, c$ are in A.P. and $a+b+c=60$. The numbers $(a-2), b, (c+3)$ are in G.P., then which of the following is not the possible value of $a^2+b^2+c^2?$

If $a, b, c$ are positive integers forming an increasing $\mathrm{G}.\mathrm{P}.$, $b-a$ is a perfect cube and ${\log }_{6}a+{\log }_{6}b+{\log }_{6}c=6$, then $a+b+c$ is

The first three terms of a geometric sequence are $x, y, z$ and these have the sum equal to $42.$ If the middle term $y$ is multiplied by $\frac{5}{4}$, the numbers $x, \frac{5y}{4}, z$ now form an arithmetic sequence. The largest possible value of $x$ is

An infinite $\mathrm{G}.\mathrm{P}.$ has $2^{\mathrm{nd}}$ term $x$ and its sum is $4.$ Then $x$ belongs to 

In a $\mathrm{G}.\mathrm{P}.,$ if the ratio of the sum of the first eleven terms to the sum of the last eleven terms is $\frac{1}{8}$ and the ratio of the sum of all the terms without the first nine terms to the sum of all the terms without the last nine terms is $2$, then the number of terms in the $\mathrm{G}.\mathrm{P}.$ is