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
9451	Find $a_{5}$ of a geometric progression if $a_{1} = - 2 and r = - \frac{1}{3}$ .	1
9452	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 2 and r = 3$ .	1
9453	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 64 and r = \frac{3}{2}$ .	1
9454	Find $a_{5}$ of a geometric progression if $a_{1} = 9 and r = - 2$ .	1
9455	Find $a_{2}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	1
9456	Find $a_{3}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	1
9457	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{4}$ .	1
9458	Find $a_{8}$ of a geometric progression if $a_{1} = 730 and r = 0.9$ .	1
9459	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 3 and r = \frac{4}{3}$ .	1
9460	Find $a_{2} 3$ of a geometric progression if $a_{1} = 1 and r = 2$ .	1
9461	Find $a_{2} 2$ of a geometric progression if $a_{1} = 1 and r = 2$ .	1
9462	Find $a_{7} 0$ of a geometric progression if $a_{1} = 0 and r = 5$ .	1
9463	Find $a_{1} 6$ of a geometric progression if $a_{1} = \frac{1}{2} and r = - \frac{1}{2}$ .	1
9464	Find the sum of the first $16$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = - \frac{1}{2}$ .	1
9465	Find $a_{1} 1$ of a geometric progression if $a_{1} = 50 and r = 1$ .	1
9466	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 6 and r = - 4$ .	1
9467	Find $a_{6}$ of a geometric progression if $a_{1} = 10 and r = \frac{2}{3}$ .	1
9468	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{1} = 10 and a_{2} = 210$ .	1
9469	$a_{1} = 10, r = 1.5, S_{n} = 340, n = ?$	1
9470	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = \frac{1}{4}$ .	1
9471	Find $a_{2}$ of a geometric progression if $a_{1} = - 1 and r = - 4$ .	1
9472	Find $a_{2}$ of a geometric progression if $a_{1} = - 1 and r = 5$ .	1
9473	Find $a_{2}$ of a geometric progression if $a_{1} = \frac{3}{4} and r = \frac{1}{2}$ .	1
9474	Find $a_{2} 9$ of a geometric progression if $a_{1} = 8 and r = \frac{1}{2}$ .	1
9475	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1 and r = 2$ .	1
9476	Find $a_{6}$ of a geometric progression if $a_{1} = 512 and r = - 2$ .	1
9477	Find $a_{6}$ of a geometric progression if $a_{1} = 16 and r = 2$ .	1
9478	Find $a_{1} 0$ of a geometric progression if $a_{1} = 9 and r = - 2$ .	1
9479	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 323 and r = - \frac{1}{6}$ .	1
9480	Find $a_{6}$ of a geometric progression if $a_{1} = 0.0124 and r = 100$ .	1
9481	Find $a_{1} 2$ of a geometric progression if $a_{1} = 0 and r = - \frac{1}{2}$ .	1
9482	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1 and r = - \frac{1}{2}$ .	1
9483	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 6 and r = - 3$ .	1
9484	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = 0 and r = - \frac{1}{2}$ .	1
9485	Find $a_{3}$ of a geometric progression if $a_{1} = 8 and r = 4$ .	1
9486	Find $a_{2} 0$ of a geometric progression if $a_{1} = 6144 and r = \frac{1}{2}$ .	1
9487	Find $a_{1} 0$ of a geometric progression if $a_{1} = 6144 and r = \frac{1}{2}$ .	1
9488	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 6144 and r = \frac{1}{2}$ .	1
9489	Find the sum of the first $46656$ terms of a geometric sequence if $a_{1} = 1 and r = - 6$ .	1
9490	Find $a_{8}$ of a geometric progression if $a_{1} = 4 and r = \frac{2}{3}$ .	1
9491	Find $a_{3}$ of a geometric progression if $a_{1} = 10 and r = 4$ .	1
9492	Find $a_{5}$ of a geometric progression if $a_{1} = 50 and r = \frac{1}{3}$ .	1
9493	Find $a_{5}$ of a geometric progression if $a_{1} = 48 and r = \frac{1}{3}$ .	1
9494	Find $a_{5}$ of a geometric progression if $a_{1} = 432 and r = \frac{1}{3}$ .	1
9495	Find $a_{5}$ of a geometric progression if $a_{1} = 500 and r = \frac{1}{5}$ .	1
9496	Find $a_{5}$ of a geometric progression if $a_{1} = 2500 and r = \frac{1}{5}$ .	1
9497	Find $a_{2} 0$ of a geometric progression if $a_{1} = 47000 and r = 0.98$ .	1
9498	Find $a_{2} 0$ of a geometric progression if $a_{1} = 47000 and r = 0.96$ .	1
9499	Find $a_{2} 0$ of a geometric progression if $a_{1} = 47000 and r = 0.95$ .	1
9500	Find $a_{4}$ of a geometric progression if $a_{1} = 25 and r = 5$ .	1