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
10801	Find the sum of the first $39$ terms of a geometric sequence if $a_{1} = 5 and r = 0.9$ .	1
10802	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = - 2 and r = - 1.383$ .	1
10803	Find $a_{1} 44$ of a geometric progression if $a_{1} = 0.015 and r = 0.015$ .	1
10804	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 100 and r = 0.75$ .	1
10805	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 100 and r = 0.75$ .	1
10806	Find $a_{6}$ of a geometric progression if $a_{1} = 120 and r = - \frac{1}{2}$ .	1
10807	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 120 and r = - \frac{1}{2}$ .	1
10808	Find $a_{6}$ of a geometric progression if $a_{1} = 4 and r = 5$ .	1
10809	Find $a_{8}$ of a geometric progression if $a_{1} = - 9 and r = - \frac{1}{2}$ .	1
10810	$a_{1} = 32, r = \frac{1}{2}, a_{n} = \frac{1}{32}, n = ?$	1
10811	Find $a_{1} 2$ of a geometric progression if $a_{1} = 256 and r = \frac{1}{4}$ .	1
10812	Find the sum of the first $17$ terms of a geometric sequence if $a_{1} = 1 and r = - \frac{1}{3}$ .	1
10813	Find the sum of the first $17$ terms of a geometric sequence if $a_{1} = - 9 and r = - \frac{1}{3}$ .	1
10814	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = \frac{99}{100}$ .	1
10815	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 72 and r = - \frac{1}{6}$ .	1
10816	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 360 and r = - \frac{1}{2}$ .	1
10817	Find first element ( $a_{1}$ ) of a geometic progression if $r = 3 and a_{2} = - 3$ .	1
10818	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 7 and r = \frac{1}{4}$ .	1
10819	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1000 and r = 1.4$ .	1
10820	$a_{1} = \frac{1}{64}, r = 4, S_{n} = 16, n = ?$	1
10821	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = - \frac{1}{5}$ .	1
10822	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 64 and a_{4} = 1$ .	1
10823	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 72 and a_{6} = \frac{1}{18}$ .	1
10824	Find $a_{1} 5$ of a geometric progression if $a_{1} = 0.00023 and r = 1.2$ .	1
10825	Find first element ( $a_{1}$ ) of a geometic progression if $r = 3 and a_{7} = 1458$ .	1
10826	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{9}{4}$ .	1
10827	Find $a_{2}$ of a geometric progression if $a_{1} = \frac{1}{9} and r = \frac{1}{9}$ .	1
10828	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = \frac{1}{9}$ .	1
10829	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{1}{4}$ .	1
10830	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 5 and r = - \frac{1}{3}$ .	1
10831	Find $a_{8}$ of a geometric progression if $a_{1} = 4000 and r = \frac{3}{2}$ .	1
10832	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 2 and r = \frac{1}{3}$ .	1
10833	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1215 and r = \frac{1}{3}$ .	1
10834	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = - 4$ .	1
10835	Find $a_{6}$ of a geometric progression if $a_{1} = 100 and r = 1.5$ .	1
10836	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 20 and r = \frac{4}{5}$ .	1
10837	Find $a_{5}$ of a geometric progression if $a_{1} = - 2 and r = 7$ .	1
10838	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{1} = 4 and a_{6} = 27$ .	1
10839	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 88 and r = 2$ .	1
10840	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 88 and r = 2$ .	1
10841	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 80 and r = 2$ .	1
10842	Find $a_{1} 4$ of a geometric progression if $a_{1} = 4 and r = 3$ .	1
10843	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0.0768 and r = 2$ .	1
10844	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0.007813 and r = 2$ .	1
10845	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 43 and r = 2$ .	1
10846	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{625}{4} and r = 2$ .	1
10847	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = \frac{81}{64} and r = \frac{2}{3}$ .	1
10848	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{1}{50} and r = 2$ .	1
10849	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 0.023 and r = 2$ .	1
10850	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 21 and r = 2$ .	1