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
9551	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = - 3$ .	1
9552	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 2 and r = - 3$ .	1
9553	$a_{1} = 432, r = 0.1667, a_{1} = ?, r = ?$	1
9554	Find $a_{4}$ of a geometric progression if $a_{1} = 64 and r = 1.333$ .	1
9555	Find $a_{4}$ of a geometric progression if $a_{1} = 64 and r = 1.333$ .	1
9556	Find common ratio ( $r$ ) in geometic progression if $a_{1} = \frac{182}{5} and a_{3} = 13.1$ .	1
9557	Find $a_{1} 1$ of a geometric progression if $a_{1} = \frac{32}{9} and r = - \frac{2}{3}$ .	1
9558	Find $a_{2} 4$ of a geometric progression if $a_{1} = 2 and r = 2$ .	1
9559	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 500 and r = 0.8$ .	1
9560	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{3} = 120 and a_{5} = \frac{384}{5}$ .	1
9561	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{4} = 216 and a_{6} = 96$ .	1
9562	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 1200 and a_{4} = 1728$ .	1
9563	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{6} = 45 and a_{8} = 71$ .	1
9564	Find $a_{5}$ of a geometric progression if $a_{1} = 50000 and r = \frac{27}{25}$ .	1
9565	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = \frac{1}{10}$ .	1
9566	Find $a_{5}$ of a geometric progression if $a_{1} = - \frac{5}{6} and r = - \frac{5}{6}$ .	1
9567	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = - \frac{5}{6}$ .	1
9568	Find $a_{1}$ of a geometric progression if $a_{1} = 1 and r = - \frac{5}{6}$ .	1
9569	Find $a_{2}$ of a geometric progression if $a_{1} = - \frac{1}{9} and r = - 3$ .	1
9570	Find $a_{4}$ of a geometric progression if $a_{1} = - \frac{1}{9} and r = - 3$ .	1
9571	Find $a_{6}$ of a geometric progression if $a_{1} = - \frac{1}{9} and r = - 3$ .	1
9572	Find $a_{8}$ of a geometric progression if $a_{1} = 10 and r = \frac{1}{5}$ .	1
9573	Find $a_{1} 0$ of a geometric progression if $a_{1} = 6 and r = - 3$ .	1
9574	Find $a_{1} 3$ of a geometric progression if $a_{1} = 0 and r = 1$ .	1
9575	Find $a_{4}$ of a geometric progression if $a_{1} = 648 and r = 3$ .	1
9576	Find $a_{8}$ of a geometric progression if $a_{1} = 648 and r = - 3$ .	1
9577	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 648 and r = 3$ .	1
9578	Find $a_{1} 1$ of a geometric progression if $a_{1} = 1000 and r = 1.005$ .	1
9579	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{3} = \frac{16}{3} and a_{5} = \frac{64}{27}$ .	1
9580	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{1} = 3 and a_{4} = 24$ .	1
9581	Find $a_{2}$ of a geometric progression if $a_{1} = 24 and r = 2$ .	1
9582	Find first element ( $a_{1}$ ) of a geometic progression if $r = - 3 and a_{2} = - 6$ .	1
9583	Find first element ( $a_{1}$ ) of a geometic progression if $r = 2 and a_{2} = - 8$ .	1
9584	Find first element ( $a_{1}$ ) of a geometic progression if $r = 2 and a_{4} = - 432$ .	1
9585	Find first element ( $a_{1}$ ) of a geometic progression if $r = 6 and a_{4} = - 432$ .	1
9586	Find $a_{4}$ of a geometric progression if $a_{1} = 2 and r = \frac{33}{100}$ .	1
9587	Find $a_{9}$ of a geometric progression if $a_{1} = 16 and r = \frac{1}{2}$ .	1
9588	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 1 and r = 1.075$ .	1
9589	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 20 and r = \frac{1}{3}$ .	1
9590	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 100 and r = - \frac{3}{5}$ .	1
9591	Find $a_{5}$ of a geometric progression if $a_{1} = 9 and r = 2$ .	1
9592	Find $a_{3}$ of a geometric progression if $a_{1} = \frac{131}{5} and r = \frac{5}{4}$ .	1
9593	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = \frac{1}{3}$ .	1
9594	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = \frac{1}{3}$ .	1
9595	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = \frac{1}{3}$ .	1
9596	Find $a_{1} 7$ of a geometric progression if $a_{1} = 16 and r = 1.75$ .	1
9597	Find $a_{4}$ of a geometric progression if $a_{1} = 14 and r = 2$ .	1
9598	Find the sum of the first $31$ terms of a geometric sequence if $a_{1} = \frac{1}{20} and r = 2$ .	1
9599	Find $a_{1} 0$ of a geometric progression if $a_{1} = 3 and r = - \frac{4}{5}$ .	1
9600	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 12 and r = 3$ .	1