The G.M.of two numbers exceeds their H.M. by $\frac{6}{5},$ the A.M. exceeds G.M. by $\frac{3}{2}$.Then the two numbers are.

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 sequence, if ${\mathrm{t}}_{\mathrm{n}}=\frac{5^{n-2}}{7^{n-3}},$ verify whether the sequence is a G.P. If it is a G.P, find its first term and the common ratio.

Find three numbers in G.P. such that their sum is $35$ and their product is $1000$ .

Find five numbers in G.P. such that their product is $243$ and sum of second and fourth number is $10$

For a sequence $S_n=4\left(7^n-1\right)$ verify that the sequence is a G.P.

Find $2+22+222+2222+....+$upto $n$ terms