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
10601	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{9}{10}$ .	1
10602	Find $a_{4}$ of a geometric progression if $a_{1} = 9 and r = - \frac{1}{3}$ .	1
10603	Find $a_{9} 9999999$ of a geometric progression if $a_{1} = 1 and r = \frac{4}{3}$ .	1
10604	Find $a_{1}$ of a geometric progression if $a_{1} = 1 and r = \frac{2}{3}$ .	1
10605	$a_{1} = 1, r = 2, a_{n} = 2, n = ?$	1
10606	$a_{1} = 1, r = 2, S_{n} = 16, n = ?$	1
10607	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 48 and r = \frac{5}{4}$ .	1
10608	Find $a_{1} 0$ of a geometric progression if $a_{1} = 48000 and r = 1.05$ .	1
10609	Find $a_{2}$ of a geometric progression if $a_{1} = 9 and r = - \frac{1}{2}$ .	1
10610	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{8} = 512 and a_{3} = 16$ .	1
10611	$a_{1} = \frac{8}{3}, r = \frac{3}{2}, S_{n} = 2500, n = ?$	1
10612	Find $a_{9}$ of a geometric progression if $a_{1} = 1024 and r = \frac{1}{2}$ .	1
10613	Find $a_{6}$ of a geometric progression if $a_{1} = 32 and r = \frac{3}{2}$ .	1
10614	Find $a_{3}$ of a geometric progression if $a_{1} = - 1 and r = \frac{1}{2}$ .	1
10615	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 12 and r = 2$ .	1
10616	Find $a_{9}$ of a geometric progression if $a_{1} = 7300000000 and r = 1.012$ .	1
10617	Find $a_{6}$ of a geometric progression if $a_{1} = - 4 and r = 4$ .	1
10618	Find $a_{6}$ of a geometric progression if $a_{1} = - 4 and r = 3$ .	1
10619	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 18 and r = - \frac{1}{2}$ .	1
10620	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = 3$ .	1
10621	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 384 and r = \frac{5}{4}$ .	1
10622	Find $a_{2} 4$ of a geometric progression if $a_{1} = 96 and r = 48$ .	1
10623	Find $a_{7}$ of a geometric progression if $a_{1} = 7 and r = 4$ .	1
10624	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 2 and a_{5} = \frac{1}{4}$ .	1
10625	Find $a_{6}$ of a geometric progression if $a_{1} = 40 and r = \frac{1}{10}$ .	1
10626	Find first element ( $a_{1}$ ) of a geometic progression if $r = - \frac{1}{2} and a_{3} = 8$ .	1
10627	Find $a_{8}$ of a geometric progression if $a_{1} = 9 and r = 6$ .	1
10628	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = \frac{1}{16} and r = - 2$ .	1
10629	Find $a_{4} 0$ of a geometric progression if $a_{1} = 2352 and r = 1.07$ .	1
10630	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = - \frac{2}{7} and r = - \frac{2}{7}$ .	1
10631	Find the sum of the first $18$ terms of a geometric sequence if $a_{1} = 16 and r = 2$ .	1
10632	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 3 and r = 10$ .	1
10633	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 40 and r = - 28$ .	1
10634	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = - \frac{2}{5}$ .	1
10635	Find $a_{1} 1$ of a geometric progression if $a_{1} = 1 and r = - 5$ .	1
10636	Find $a_{5}$ of a geometric progression if $a_{1} = 4 and r = - 2$ .	1
10637	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = - \frac{1}{2}$ .	1
10638	Find $a_{8}$ of a geometric progression if $a_{1} = 5 and r = 4$ .	1
10639	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 65536 and r = - \frac{1}{4}$ .	1
10640	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 65536 and r = \frac{1}{4}$ .	1
10641	Find $a_{9}$ of a geometric progression if $a_{1} = 1536 and r = \frac{1}{2}$ .	1
10642	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 96 and r = \frac{1}{2}$ .	1
10643	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 0.125 and r = - 2$ .	1
10644	Find $a_{6}$ of a geometric progression if $a_{1} = 0.125 and r = - 2$ .	1
10645	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 256 and r = \frac{1}{4}$ .	1
10646	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 32 and r = \frac{5}{2}$ .	1
10647	Find the sum of the first $63$ terms of a geometric sequence if $a_{1} = 1.004 and r = 1$ .	1
10648	Find $a_{5}$ of a geometric progression if $a_{1} = 50 and r = \frac{4}{5}$ .	1
10649	Find $a_{3}$ of a geometric progression if $a_{1} = 1 and r = \frac{5}{11}$ .	1
10650	Find $a_{5}$ of a geometric progression if $a_{1} = - 9 and r = - \frac{2}{3}$ .	1