Maharashtra Board Solutions for Chapter: Sequences and Series, Exercise 7: MISCELLANEOUS EXERCISE

In a G.P., the fourth term is $48$ and the eighth term is $768$. Find the tenth term.

Find the sum of the first $5$ terms of the G.P. whose first term is $1$ and common ratio is $\frac{2}{3}$.

For a G.P with positive terms, $a=\frac{4}{3}$ and $t_7=\frac{243}{1024},$ find the value of $r$ correct to two places of the decimal.

For a G.P. if $t_2=7,t_4=1575$, find $a$ and express the answer as a fraction in lowest form.

If for a G.P. $t_3=\frac{1}{3},t_6=\frac{1}{81}$, find common ratio and express the answer as a fraction in lowest form.

Find $k$ so that $k-1, k, k+2$ are consecutive terms of a G.P.

If $p^{th},q^{th} \mathrm{and} r^{th}$ terms of a G.P. are  $x,y,z$ respectively. Find the value of $x^{q-r}·y^{r-p}·z^{p-q}$

If the sum of infinite terms of series: $1+\frac{4}{5}+\frac{7}{25}+\frac{10}{125}+\frac{13}{625}+\dots$ is $\frac{k}{16}$, then find the value of $k$.