Geometric sequences

(the database of solved problems)

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

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ID	Problem	Count
9801	Find $a_{4} 5$ of a geometric progression if $a_{1} = 50000 and r = 0.9808$ .	1
9802	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{8}{5} and r = \frac{9}{10}$ .	1
9803	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 262144 and r = \frac{1}{8}$ .	1
9804	$a_{1} = \frac{5}{2}, r = 2, a_{n} = 11, n = ?$	1
9805	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{3}{5} and r = \frac{33}{50}$ .	1
9806	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{3}{5} and r = \frac{33}{50}$ .	1
9807	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{1}{4} and r = \frac{1}{4}$ .	1
9808	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 2 and r = - 2$ .	1
9809	Find $a_{7}$ of a geometric progression if $a_{1} = 512 and r = \frac{1}{2}$ .	1
9810	Find $a_{3}$ of a geometric progression if $a_{1} = 50 and r = 80$ .	1
9811	Find $a_{5} 0$ of a geometric progression if $a_{1} = 80 and r = 3$ .	1
9812	Find $a_{5} 0$ of a geometric progression if $a_{1} = 3 and r = 90$ .	1
9813	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = 15$ .	1
9814	Find $a_{2}$ of a geometric progression if $a_{1} = 15 and r = 10$ .	1
9815	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 16 and a_{2} = 8$ .	1
9816	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 15 and r = \frac{7}{10}$ .	1
9817	$a_{1} = 8, r = 5, a_{n} = 3125000, n = ?$	1
9818	$a_{1} = \frac{19141}{100}, r = 1.031, a_{n} = 1020, n = ?$	1
9819	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = 15 and a_{7} = \frac{405}{64}$ .	1
9820	Find common ratio ( $r$ ) in geometic progression if $a_{1} = \frac{41}{10} and a_{2} = \frac{87}{20}$ .	1
9821	Find $a_{2}$ of a geometric progression if $a_{1} = \frac{41}{10} and r = 1.061$ .	1
9822	$a_{1} = 5, r = 3, a_{1} = ?, r = ?$	1
9823	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{3}{2}$ .	1
9824	Find $a_{5}$ of a geometric progression if $a_{1} = 10 and r = 1$ .	1
9825	Find $a_{6}$ of a geometric progression if $a_{1} = 50 and r = - 1$ .	1
9826	Find first element ( $a_{1}$ ) of a geometic progression if $r = 4 and a_{7} = - 10992$ .	1
9827	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 10 and r = \frac{5}{3}$ .	1
9828	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = \frac{5}{3}$ .	1
9829	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 3 and r = \frac{5}{2}$ .	1
9830	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{5}{3} and r = 3$ .	1
9831	Find $a_{6}$ of a geometric progression if $a_{1} = 8 and r = \frac{3}{4}$ .	1
9832	Find $a_{5}$ of a geometric progression if $a_{1} = 4 and r = \frac{3}{4}$ .	1
9833	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 5 and r = 1.2$ .	1
9834	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 100 and r = 0.041$ .	1
9835	Find $a_{1} 2$ of a geometric progression if $a_{1} = 100 and r = 0.041$ .	1
9836	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1 and r = 1.041$ .	1
9837	Find $a_{1} 2$ of a geometric progression if $a_{1} = 96 and r = - 2$ .	1
9838	Find $a_{9}$ of a geometric progression if $a_{1} = - 3125 and r = \frac{1}{5}$ .	1
9839	Find $a_{8}$ of a geometric progression if $a_{1} = - \frac{1}{250} and r = 4$ .	1
9840	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = - 8 and r = \frac{1}{3}$ .	1
9841	Find the sum of the first $23$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
9842	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 0 and r = 3$ .	1
9843	Find $a_{6}$ of a geometric progression if $a_{1} = \frac{1}{2} and r = 2$ .	1
9844	Find $a_{1} 0$ of a geometric progression if $a_{1} = 16 and r = 2$ .	1
9845	Find $a_{8}$ of a geometric progression if $a_{1} = - 6 and r = - \frac{1}{2}$ .	1
9846	Find $a_{6}$ of a geometric progression if $a_{1} = - 34816 and r = \frac{1}{2}$ .	1
9847	Find $a_{1} 2$ of a geometric progression if $a_{1} = 96 and r = \frac{1}{2}$ .	1
9848	Find $a_{4} 6$ of a geometric progression if $a_{1} = 310 and r = 0.98$ .	1
9849	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	1
9850	Find $a_{4}$ of a geometric progression if $a_{1} = 150 and r = \frac{3}{2}$ .	1