Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
9801	Find $a_{1} 4$ of a geometric progression if $a_{1} = 2 and r = 5$ .	1
9802	Find $a_{1} 2$ of a geometric progression if $a_{1} = 36 and r = \frac{1}{2}$ .	1
9803	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 32 and r = \frac{1}{4}$ .	1
9804	Find $a_{6}$ of a geometric progression if $a_{1} = 128 and r = \frac{1}{2}$ .	1
9805	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 80 and r = - \frac{1}{2}$ .	1
9806	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{1}{50} and r = \frac{6}{5}$ .	1
9807	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 40 and r = \frac{9}{10}$ .	1
9808	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 46000 and r = \frac{109}{100}$ .	1
9809	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{32} and r = - 2$ .	1
9810	Find $a_{5}$ of a geometric progression if $a_{1} = 5 and r = \frac{6}{5}$ .	1
9811	Find $a_{5}$ of a geometric progression if $a_{1} = 5 and r = \frac{6}{5}$ .	1
9812	Find $a_{3}$ of a geometric progression if $a_{1} = 5 and r = \frac{6}{5}$ .	1
9813	Find $a_{4}$ of a geometric progression if $a_{1} = 5 and r = \frac{6}{5}$ .	1
9814	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{9}{2} and r = 6$ .	1
9815	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 5 and r = \frac{1}{2}$ .	1
9816	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 6 and r = \frac{1}{3}$ .	1
9817	Find $a_{3} 2$ of a geometric progression if $a_{1} = 2 and r = 8$ .	1
9818	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 2 and r = 4$ .	1
9819	Find $a_{7}$ of a geometric progression if $a_{1} = 8 and r = 3$ .	1
9820	Find $a_{7} 0$ of a geometric progression if $a_{1} = 1 and r = 2$ .	1
9821	Find $a_{9}$ of a geometric progression if $a_{1} = 0 and r = 7$ .	1
9822	Find $a_{9}$ of a geometric progression if $a_{1} = 64 and r = 7$ .	1
9823	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 10000 and r = \frac{26}{25}$ .	1
9824	Find $a_{1} 2$ of a geometric progression if $a_{1} = 10 and r = - 5$ .	1
9825	Find $a_{4}$ of a geometric progression if $a_{1} = 10 and r = \frac{11}{50}$ .	1
9826	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = 2$ .	1
9827	Find $a_{2} 10000$ of a geometric progression if $a_{1} = 50 and r = 25$ .	1
9828	Find the sum of the first $210000$ terms of a geometric sequence if $a_{1} = 50 and r = 25$ .	1
9829	Find $a_{1} 000000000000000$ of a geometric progression if $a_{1} = 50 and r = \frac{1}{2}$ .	1
9830	$a_{1} = 12, r = 55, a_{1} = ?, r = ?$	1
9831	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 2 and r = \frac{1}{2}$ .	1
9832	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = - 2 and r = \frac{1}{2}$ .	1
9833	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 6 and a_{2} = 28$ .	1
9834	Find $a_{3}$ of a geometric progression if $a_{1} = 6 and r = \frac{14}{3}$ .	1
9835	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = \frac{8}{3}$ .	1
9836	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = 1$ .	1
9837	Find $a_{3} 2$ of a geometric progression if $a_{1} = 0.06 and r = 0.06$ .	1
9838	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{2} and r = - \frac{1}{6}$ .	1
9839	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 100000 and r = \frac{13}{10}$ .	1
9840	$a_{1} = 256, r = 0.707, a_{n} = 1.414, n = ?$	1
9841	Find $a_{5}$ of a geometric progression if $a_{1} = 75 and r = \frac{1}{5}$ .	1
9842	Find $a_{5}$ of a geometric progression if $a_{1} = 75 and r = 5$ .	1
9843	Find $a_{5}$ of a geometric progression if $a_{1} = 75 and r = 2$ .	1
9844	Find $a_{5}$ of a geometric progression if $a_{1} = 75 and r = 1$ .	1
9845	Find $a_{5}$ of a geometric progression if $a_{1} = 75 and r = \frac{3}{2}$ .	1
9846	Find $a_{6}$ of a geometric progression if $a_{1} = 972 and r = 3$ .	1
9847	Find $a_{5}$ of a geometric progression if $a_{1} = 1536 and r = 2$ .	1
9848	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1536 and r = - 4$ .	1
9849	Find $a_{1} 2$ of a geometric progression if $a_{1} = - 5 and r = - 3$ .	1
9850	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 243 and r = - \frac{2}{3}$ .	1