Given $a_1,a_2,a_3.....$ form an increasing geometric progression with common ratio $r$ such that $log_8a_1 + log_8a_2 +.....+ log_8a_{12} = 2014,$ then the number of ordered pairs of integers $(a_1, r)$ is equal to
$44$
$45$
$46$
$47$
The sum of first two terms of a $G.P.$ is $1$ and every term of this series is twice of its previous term, then the first term will be
Find the sum of the following series up to n terms:
$5+55+555+\ldots$
Let $a_{n}$ be the $n^{\text {th }}$ term of a G.P. of positive terms.
If $\sum\limits_{n=1}^{100} a_{2 n+1}=200$ and $\sum\limits_{n=1}^{100} a_{2 n}=100,$ then $\sum\limits_{n=1}^{200} a_{n}$ is equal to
The product $(32)(32)^{1/6}(32)^{1/36} ...... to\,\, \infty $ is
Which term of the following sequences:
$\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683} ?$