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
9401	Find $a_{1} 0$ of a geometric progression if $a_{1} = 18 and r = \frac{5}{9}$ .	1
9402	Find $a_{3} 0$ of a geometric progression if $a_{1} = 2 and r = 1$ .	1
9403	Find $a_{7}$ of a geometric progression if $a_{1} = 6 and r = 4$ .	1
9404	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{1}{4}$ .	1
9405	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{8} = \frac{2}{3} and a_{5} = 18$ .	1
9406	Find $a_{2} 5$ of a geometric progression if $a_{1} = 6 and r = 2$ .	1
9407	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 729 and r = \frac{1}{3}$ .	1
9408	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 729 and r = \frac{1}{3}$ .	1
9409	Find $a_{6}$ of a geometric progression if $a_{1} = 1 and r = \frac{11}{10}$ .	1
9410	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{11}{10}$ .	1
9411	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 15 and r = - 14$ .	1
9412	Find $a_{4}$ of a geometric progression if $a_{1} = - 3 and r = - 5$ .	1
9413	Find $a_{7}$ of a geometric progression if $a_{1} = 6 and r = \frac{4}{3}$ .	1
9414	Find $a_{1}$ of a geometric progression if $a_{1} = 3 and r = \frac{1}{2}$ .	1
9415	Find $a_{2}$ of a geometric progression if $a_{1} = 3 and r = \frac{1}{2}$ .	1
9416	Find $a_{7}$ of a geometric progression if $a_{1} = 0 and r = 2$ .	1
9417	Find $a_{7}$ of a geometric progression if $a_{1} = 243 and r = \frac{2}{3}$ .	1
9418	Find $a_{7}$ of a geometric progression if $a_{1} = 5 and r = \frac{3}{5}$ .	1
9419	Find $a_{8}$ of a geometric progression if $a_{1} = 500 and r = \frac{4}{5}$ .	1
9420	Find $a_{5}$ of a geometric progression if $a_{1} = 0 and r = \frac{6}{5}$ .	1
9421	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{8} = 6250 and a_{4} = 10$ .	1
9422	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 26 and r = 5$ .	1
9423	Find $a_{8}$ of a geometric progression if $a_{1} = 26 and r = 5$ .	1
9424	Find $a_{9}$ of a geometric progression if $a_{1} = 14 and r = - 6$ .	1
9425	Find $a_{1} 3$ of a geometric progression if $a_{1} = 12 and r = 2$ .	1
9426	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{125}{8} and r = \frac{1}{2}$ .	1
9427	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{125}{8} and r = \frac{1}{2}$ .	1
9428	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = 125 and a_{10} = \frac{125}{64}$ .	1
9429	Find $a_{6}$ of a geometric progression if $a_{1} = - \frac{3}{4} and r = - \frac{1}{4}$ .	1
9430	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 1 and r = - \frac{1}{2}$ .	1
9431	$a_{1} = 2, r = 5, a_{1} = ?, r = ?$	1
9432	Find $a_{2}$ of a geometric progression if $a_{1} = - 4 and r = 2$ .	1
9433	Find $a_{4}$ of a geometric progression if $a_{1} = - 54 and r = \frac{4}{3}$ .	1
9434	Find $a_{4}$ of a geometric progression if $a_{1} = 11 and r = 10$ .	1
9435	Find $a_{3}$ of a geometric progression if $a_{1} = 8 and r = - 5$ .	1
9436	Find $a_{4}$ of a geometric progression if $a_{1} = - \frac{1}{16} and r = 2$ .	1
9437	Find $a_{4}$ of a geometric progression if $a_{1} = 2400 and r = \frac{1}{3}$ .	1
9438	Find $a_{3}$ of a geometric progression if $a_{1} = 1 and r = \frac{5}{2}$ .	1
9439	Find $a_{3}$ of a geometric progression if $a_{1} = \frac{64}{25} and r = \frac{5}{2}$ .	1
9440	Find $a_{1}$ of a geometric progression if $a_{1} = 1875 and r = 0.2$ .	1
9441	Find $a_{3}$ of a geometric progression if $a_{1} = 1875 and r = 0.2$ .	1
9442	Find $a_{4}$ of a geometric progression if $a_{1} = 1451607 and r = 1.02$ .	1
9443	Find $a_{3}$ of a geometric progression if $a_{1} = \frac{9}{8} and r = \frac{1}{5}$ .	1
9444	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 55000 and r = \frac{3}{2}$ .	1
9445	Find $a_{3}$ of a geometric progression if $a_{1} = 48 and r = 12$ .	1
9446	Find $a_{7}$ of a geometric progression if $a_{1} = - 17 and r = 3$ .	1
9447	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{1}{2} and a_{8} = - \frac{5}{8}$ .	1
9448	Find $a_{1} 2$ of a geometric progression if $a_{1} = - 80 and r = \frac{1}{2}$ .	1
9449	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 48 and r = - 2$ .	1
9450	$a_{1} = 8, r = \frac{1}{2}, S_{n} = 15, n = ?$	1