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
10051	Find $a_{1} 6$ of a geometric progression if $a_{1} = 50000 and r = \frac{26}{25}$ .	1
10052	Find $a_{4}$ of a geometric progression if $a_{1} = 14 and r = \frac{1}{3}$ .	1
10053	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{119}{5}$ .	1
10054	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{3}{10} and r = \frac{1}{2}$ .	1
10055	Find the sum of the first $175$ terms of a geometric sequence if $a_{1} = 515036 and r = 1.08$ .	1
10056	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{3}{10} and r = \frac{3}{5}$ .	1
10057	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - \frac{2}{25} and r = - \frac{2}{5}$ .	1
10058	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{1}{5} and r = \frac{3}{5}$ .	1
10059	Find $a_{3} 0$ of a geometric progression if $a_{1} = 14 and r = 2$ .	1
10060	Find the sum of the first $26$ terms of a geometric sequence if $a_{1} = 1987 and r = 0.03$ .	1
10061	Find $a_{3}$ of a geometric progression if $a_{1} = 50000 and r = \frac{11}{10}$ .	1
10062	Find the sum of the first $60$ terms of a geometric sequence if $a_{1} = 10186 and r = 1.006$ .	1
10063	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 75 and r = \frac{1}{2}$ .	1
10064	Find $a_{4}$ of a geometric progression if $a_{1} = 402050 and r = \frac{51}{50}$ .	1
10065	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 3 and r = \frac{2}{3}$ .	1
10066	Find $a_{1} 2$ of a geometric progression if $a_{1} = 81 and r = - \frac{1}{3}$ .	1
10067	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{16}{9} and r = \frac{3}{2}$ .	1
10068	Find $a_{7}$ of a geometric progression if $a_{1} = 32 and r = \frac{1}{4}$ .	1
10069	Find the sum of the first $50$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{10}{11}$ .	1
10070	$a_{1} = 6, r = 2, a_{n} = 768, n = ?$	1
10071	$a_{1} = 8, r = 2, S_{n} = 32760, n = ?$	1
10072	Find $a_{4}$ of a geometric progression if $a_{1} = 524059 and r = 1.02$ .	1
10073	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{3}$ .	1
10074	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 9 and r = \frac{1}{3}$ .	1
10075	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{3}{2} and r = 4$ .	1
10076	Find $a_{6}$ of a geometric progression if $a_{1} = 27 and r = \frac{3}{5}$ .	1
10077	Find $a_{6}$ of a geometric progression if $a_{1} = 27 and r = \frac{5}{3}$ .	1
10078	Find $a_{1} 5$ of a geometric progression if $a_{1} = 2 and r = - 4$ .	1
10079	Find $a_{1} 2$ of a geometric progression if $a_{1} = 2 and r = - 4$ .	1
10080	Find $a_{9}$ of a geometric progression if $a_{1} = 9 and r = - 2$ .	1
10081	Find $a_{4}$ of a geometric progression if $a_{1} = 20 and r = \frac{3}{4}$ .	1
10082	Find $a_{1} 0$ of a geometric progression if $a_{1} = 7 and r = - \frac{2}{5}$ .	1
10083	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = 7 and r = - \frac{2}{5}$ .	1
10084	Find $a_{8}$ of a geometric progression if $a_{1} = - 1 and r = - 6$ .	1
10085	Find $a_{2} 3$ of a geometric progression if $a_{1} = 160000 and r = 0.1$ .	1
10086	$a_{1} = 0.01, r = 1.5, a_{1} = ?, r = ?$	1
10087	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0 and r = \frac{53}{50}$ .	1
10088	Find the sum of the first $16384$ terms of a geometric sequence if $a_{1} = - 16 and r = - 4$ .	1
10089	$a_{1} = 4.1, r = 2, a_{n} = 61.5, n = ?$	1
10090	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 41000000000 and r = 1.03$ .	1
10091	Find $a_{9} 223372036854775807$ of a geometric progression if $a_{1} = \frac{1}{3} and r = \frac{2}{3}$ .	1
10092	Find $a_{1} 8$ of a geometric progression if $a_{1} = 3 and r = 0.5774$ .	1
10093	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 4 and r = - \frac{4}{5}$ .	1
10094	Find first element ( $a_{1}$ ) of a geometic progression if $r = 5 and a_{4} = 500$ .	1
10095	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = 500 and a_{7} = 62500$ .	1
10096	Find $a_{3}$ of a geometric progression if $a_{1} = - 8 and r = - 1$ .	1
10097	Find $a_{3}$ of a geometric progression if $a_{1} = 16 and r = \frac{3}{2}$ .	1
10098	Find $a_{1} 2$ of a geometric progression if $a_{1} = 12 and r = - 5$ .	1
10099	Find $a_{1} 0$ of a geometric progression if $a_{1} = 0.375 and r = 8$ .	1
10100	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1000 and r = \frac{1}{2}$ .	1