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
10551	Find $a_{8}$ of a geometric progression if $a_{1} = - 9 and r = - \frac{1}{2}$ .	1
10552	$a_{1} = 32, r = \frac{1}{2}, a_{n} = \frac{1}{32}, n = ?$	1
10553	Find $a_{1} 2$ of a geometric progression if $a_{1} = 256 and r = \frac{1}{4}$ .	1
10554	Find the sum of the first $17$ terms of a geometric sequence if $a_{1} = 1 and r = - \frac{1}{3}$ .	1
10555	Find the sum of the first $17$ terms of a geometric sequence if $a_{1} = - 9 and r = - \frac{1}{3}$ .	1
10556	Find $a_{5}$ of a geometric progression if $a_{1} = 1 and r = \frac{99}{100}$ .	1
10557	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 72 and r = - \frac{1}{6}$ .	1
10558	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 360 and r = - \frac{1}{2}$ .	1
10559	Find first element ( $a_{1}$ ) of a geometic progression if $r = 3 and a_{2} = - 3$ .	1
10560	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 7 and r = \frac{1}{4}$ .	1
10561	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1000 and r = 1.4$ .	1
10562	$a_{1} = \frac{1}{64}, r = 4, S_{n} = 16, n = ?$	1
10563	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = - \frac{1}{5}$ .	1
10564	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 64 and a_{4} = 1$ .	1
10565	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 72 and a_{6} = \frac{1}{18}$ .	1
10566	Find $a_{1} 5$ of a geometric progression if $a_{1} = 0.00023 and r = 1.2$ .	1
10567	Find first element ( $a_{1}$ ) of a geometic progression if $r = 3 and a_{7} = 1458$ .	1
10568	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{9}{4}$ .	1
10569	Find $a_{2}$ of a geometric progression if $a_{1} = \frac{1}{9} and r = \frac{1}{9}$ .	1
10570	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = \frac{1}{9}$ .	1
10571	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{1}{4}$ .	1
10572	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 5 and r = - \frac{1}{3}$ .	1
10573	Find $a_{8}$ of a geometric progression if $a_{1} = 4000 and r = \frac{3}{2}$ .	1
10574	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 2 and r = \frac{1}{3}$ .	1
10575	Find $a_{1} 2$ of a geometric progression if $a_{1} = 1215 and r = \frac{1}{3}$ .	1
10576	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 5 and r = - 4$ .	1
10577	Find $a_{6}$ of a geometric progression if $a_{1} = 100 and r = 1.5$ .	1
10578	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 20 and r = \frac{4}{5}$ .	1
10579	Find $a_{5}$ of a geometric progression if $a_{1} = - 2 and r = 7$ .	1
10580	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{1} = 4 and a_{6} = 27$ .	1
10581	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 88 and r = 2$ .	1
10582	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 88 and r = 2$ .	1
10583	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 80 and r = 2$ .	1
10584	Find $a_{1} 4$ of a geometric progression if $a_{1} = 4 and r = 3$ .	1
10585	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0.0768 and r = 2$ .	1
10586	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 0.007813 and r = 2$ .	1
10587	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 43 and r = 2$ .	1
10588	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{625}{4} and r = 2$ .	1
10589	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = \frac{81}{64} and r = \frac{2}{3}$ .	1
10590	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = \frac{1}{50} and r = 2$ .	1
10591	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 0.023 and r = 2$ .	1
10592	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 21 and r = 2$ .	1
10593	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 20000 and r = 2$ .	1
10594	Find $a_{1} 6$ of a geometric progression if $a_{1} = 1 and r = 4$ .	1
10595	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{5}{2} and r = - \frac{1}{2}$ .	1
10596	Find $a_{1}$ of a geometric progression if $a_{1} = \frac{5}{2} and r = - \frac{1}{2}$ .	1
10597	$a_{1} = 1500000, r = \frac{1}{10}, a_{n} = 5, n = ?$	1
10598	Find $a_{6}$ of a geometric progression if $a_{1} = 7 and r = 4$ .	1
10599	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = 0.9259$ .	1
10600	Find the sum of the first $1000000000011110$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{1}{4}$ .	1