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
9901	Find $a_{5}$ of a geometric progression if $a_{1} = 75 and r = \frac{3}{2}$ .	1
9902	Find $a_{6}$ of a geometric progression if $a_{1} = 972 and r = 3$ .	1
9903	Find $a_{5}$ of a geometric progression if $a_{1} = 1536 and r = 2$ .	1
9904	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1536 and r = - 4$ .	1
9905	Find $a_{1} 2$ of a geometric progression if $a_{1} = - 5 and r = - 3$ .	1
9906	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 243 and r = - \frac{2}{3}$ .	1
9907	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{5}{4} and r = 2$ .	1
9908	Find $a_{4}$ of a geometric progression if $a_{1} = 42 and r = - 8$ .	1
9909	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{9}{10}$ .	1
9910	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = \frac{9}{10}$ .	1
9911	Find $a_{6}$ of a geometric progression if $a_{1} = 30 and r = \frac{4}{5}$ .	1
9912	Find $a_{2}$ of a geometric progression if $a_{1} = 30 and r = \frac{4}{5}$ .	1
9913	Find $a_{3}$ of a geometric progression if $a_{1} = 30 and r = \frac{4}{5}$ .	1
9914	Find $a_{4}$ of a geometric progression if $a_{1} = 30 and r = \frac{4}{5}$ .	1
9915	Find $a_{1} 2$ of a geometric progression if $a_{1} = - 1 and r = - 6$ .	1
9916	$a_{1} = 10, r = 0.333, a_{n} = 2222, n = ?$	1
9917	$a_{1} = 10, r = 1.5, a_{n} = 1490, n = ?$	1
9918	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 30 and r = \frac{1}{2}$ .	1
9919	Find $a_{3}$ of a geometric progression if $a_{1} = 75 and r = 3$ .	1
9920	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 32 and r = \frac{3}{2}$ .	1
9921	Find first element ( $a_{1}$ ) of a geometic progression if $r = \frac{1}{3} and a_{6} = 443$ .	1
9922	$a_{1} = 16, r = \frac{1}{2}, S_{n} = 31.94, n = ?$	1
9923	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = - \frac{1}{4}$ .	1
9924	Find $a_{1} 5$ of a geometric progression if $a_{1} = 1 and r = - \frac{1}{4}$ .	1
9925	Find $a_{6}$ of a geometric progression if $a_{1} = - \frac{1}{2} and r = - \frac{3}{2}$ .	1
9926	Find $a_{4}$ of a geometric progression if $a_{1} = - \frac{3}{2} and r = 2$ .	1
9927	Find $a_{8}$ of a geometric progression if $a_{1} = - \frac{3}{2} and r = 2$ .	1
9928	Find $a_{1} 2$ of a geometric progression if $a_{1} = - \frac{3}{2} and r = 2$ .	1
9929	Find $a_{4}$ of a geometric progression if $a_{1} = 2 and r = - \frac{1}{2}$ .	1
9930	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 20 and r = 1.3$ .	1
9931	Find the sum of the first $38$ terms of a geometric sequence if $a_{1} = 2 and r = 2$ .	1
9932	Find $a_{5}$ of a geometric progression if $a_{1} = 40000 and r = \frac{1}{20}$ .	1
9933	Find $a_{1} 4$ of a geometric progression if $a_{1} = 3 and r = 2$ .	1
9934	Find $a_{9}$ of a geometric progression if $a_{1} = 6 and r = 5$ .	1
9935	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 70000 and r = 1.015$ .	1
9936	Find the sum of the first $1000$ terms of a geometric sequence if $a_{1} = 1 and r = 2$ .	1
9937	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 6 and a_{3} = 16$ .	1
9938	Find $a_{1} 0$ of a geometric progression if $a_{1} = 20 and r = 4$ .	1
9939	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 43 and a_{2} = 38$ .	1
9940	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = 14 and r = \frac{4}{5}$ .	1
9941	Find $a_{1}$ of a geometric progression if $a_{1} = 16 and r = \frac{1}{2}$ .	1
9942	$a_{1} = 2, r = 2, S_{n} = 14, n = ?$	1
9943	$a_{1} = 6, r = \frac{1}{2}, a_{1} = ?, r = ?$	1
9944	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{2}{125} and r = 5$ .	1
9945	Find $a_{7}$ of a geometric progression if $a_{1} = 0.0008 and r = - 10$ .	1
9946	Find $a_{1} 3$ of a geometric progression if $a_{1} = 2 and r = 6$ .	1
9947	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 18 and r = \frac{1}{3}$ .	1
9948	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 5 and r = 10$ .	1
9949	Find $a_{1} 4$ of a geometric progression if $a_{1} = 5 and r = 2$ .	1
9950	Find $a_{1} 5$ of a geometric progression if $a_{1} = 5 and r = 2$ .	1