M L Aggarwal Solutions for Chapter: Sequences and Series, Exercise 5: EXERCISE 10.5

Find the $6^{th}$ term from the end of the sequence $3,-6,12,-24,\dots ,12288$.

Which term of the sequence $1,\frac{1}{3},\frac{1}{9},\dots$ is $\frac{1}{243}$?

Which term of the sequence $\frac{1}{3},\frac{1}{9},\frac{1}{27},\dots$ is $\frac{1}{19683}$?

Which term of the series $2+8+32+\dots$ is $131072$?

Find the value of $x$ such that  $x, x+3, x+9$ are first three terms of a $G.P.$

The first and the second terms of a $G.P.$ are $x^{-4}$ and $x^m$. If its $8^{th}$ term is $x^{52}$, then find the value of $m$.

The fourth term of a $G.P.$ is the square of its second term and the first term is $-3$. Determine its seventh term.

If $a,b,c$ are in $A.P.$ as well as in $G.P.$, then find the value of $a^{b-c}+b^{c-a}+c^{a-b}$.