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
10901	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 240 and r = - \frac{1}{4}$ .	1
10902	Find $a_{1} 4$ of a geometric progression if $a_{1} = 160000 and r = \frac{1}{2}$ .	1
10903	Find $a_{6}$ of a geometric progression if $a_{1} = 32 and r = 32$ .	1
10904	Find $a_{2}$ of a geometric progression if $a_{1} = 200000 and r = 1.09$ .	1
10905	Find $a_{5} 0$ of a geometric progression if $a_{1} = 200000 and r = 1.09$ .	1
10906	Find $a_{1} 1$ of a geometric progression if $a_{1} = 3 and r = 2.33$ .	1
10907	Find $a_{1} 2$ of a geometric progression if $a_{1} = 100 and r = \frac{1}{2}$ .	1
10908	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1000 and r = \frac{1}{2}$ .	1
10909	Find $a_{1} 4$ of a geometric progression if $a_{1} = 6 and r = 3$ .	1
10910	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{1} = \frac{1}{3} and a_{2} = \frac{2}{9}$ .	1
10911	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 3 and r = 3$ .	1
10912	Find $a_{1} 0$ of a geometric progression if $a_{1} = 16 and r = \frac{5}{4}$ .	1
10913	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = \frac{1}{50} and r = 2$ .	1
10914	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 4 and r = - 3$ .	1
10915	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 162 and r = 3$ .	1
10916	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = - 3$ .	1
10917	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2560 and r = \frac{1}{2}$ .	1
10918	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 9 and r = \frac{2}{3}$ .	1
10919	Find the sum of the first $31$ terms of a geometric sequence if $a_{1} = 0.05 and r = 2$ .	1
10920	Find $a_{1} 5$ of a geometric progression if $a_{1} = 4 and r = 4$ .	1
10921	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 55580 and r = 1.039$ .	1
10922	Find $a_{2}$ of a geometric progression if $a_{1} = 6 and r = \frac{59}{221}$ .	1
10923	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = 32768 and r = - \frac{1}{2}$ .	1
10924	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 729 and r = \frac{2}{3}$ .	1
10925	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{1}{2}$ .	1
10926	Find $a_{4}$ of a geometric progression if $a_{1} = - 128 and r = \frac{1}{2}$ .	1
10927	Find $a_{7}$ of a geometric progression if $a_{1} = 270 and r = \frac{3}{2}$ .	1
10928	Find the sum of the first $26$ terms of a geometric sequence if $a_{1} = 7 and r = 2$ .	1
10929	Find the sum of the first $31$ terms of a geometric sequence if $a_{1} = 0.2 and r = 2$ .	1
10930	Find $a_{3}$ of a geometric progression if $a_{1} = 0 and r = 2$ .	1
10931	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 0 and r = 2$ .	1
10932	Find $a_{4}$ of a geometric progression if $a_{1} = 81 and r = \frac{1}{9}$ .	1
10933	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{1}{4}$ .	1
10934	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 2 and r = 1$ .	1
10935	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 4 and r = 4$ .	1
10936	Find $a_{1} 5$ of a geometric progression if $a_{1} = 20 and r = \frac{1}{3}$ .	1
10937	Find $a_{1} 0$ of a geometric progression if $a_{1} = 17 and r = 5$ .	1
10938	Find $a_{4}$ of a geometric progression if $a_{1} = 2700 and r = 1.111$ .	1
10939	Find $a_{7}$ of a geometric progression if $a_{1} = 2700 and r = 1.111$ .	1
10940	Find $a_{1} 0$ of a geometric progression if $a_{1} = 110000 and r = \frac{11}{10}$ .	1
10941	Find $a_{8}$ of a geometric progression if $a_{1} = \frac{7}{3} and r = 3$ .	1
10942	Find $a_{2} 00$ of a geometric progression if $a_{1} = 10000 and r = 1.005$ .	1
10943	Find $a_{2} 00$ of a geometric progression if $a_{1} = 50000 and r = 1.005$ .	1
10944	Find $a_{2} 00$ of a geometric progression if $a_{1} = 74000 and r = 1.005$ .	1
10945	Find $a_{2}$ of a geometric progression if $a_{1} = 1990 and r = \frac{1}{2}$ .	1
10946	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 69 and r = - 7.625$ .	1
10947	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 0.005 and r = 1.15$ .	1
10948	Find $a_{1} 0$ of a geometric progression if $a_{1} = 7 and r = - 3$ .	1
10949	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{1}{36} and r = - 3$ .	1
10950	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = \frac{22}{7} and r = \frac{2}{7}$ .	1