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
10651	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 64 and r = - \frac{1}{2}$ .	1
10652	Find $a_{1}$ of a geometric progression if $a_{1} = 36 and r = \frac{1}{3}$ .	1
10653	Find $a_{1} 1$ of a geometric progression if $a_{1} = 3 and r = 12$ .	1
10654	Find $a_{1} 1$ of a geometric progression if $a_{1} = 12 and r = 3$ .	1
10655	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 7 and r = - 12$ .	1
10656	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{33}{5} and r = - 5$ .	1
10657	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 25 and r = \frac{3}{5}$ .	1
10658	$a_{1} = 27, r = \frac{1}{3}, a_{n} = \frac{1}{729}, n = ?$	1
10659	Find $a_{9}$ of a geometric progression if $a_{1} = 256 and r = \frac{3}{2}$ .	1
10660	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 256 and r = \frac{3}{2}$ .	1
10661	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 729 and r = \frac{2}{3}$ .	1
10662	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{5} = 32 and a_{10} = 1024$ .	1
10663	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{5} = 26 and a_{13} = 4096$ .	1
10664	$a_{1} = 2.072, r = 1.882, a_{n} = 7, n = ?$	1
10665	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 2.072 and a_{13} = 4096$ .	1
10666	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 1 and r = 10$ .	1
10667	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = 10$ .	1
10668	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 9 and r = 5$ .	1
10669	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 9 and r = 5$ .	1
10670	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{2}$ .	1
10671	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{2}$ .	1
10672	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 9 and r = - \frac{2}{3}$ .	1
10673	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 60 and r = \frac{9}{10}$ .	1
10674	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 4 and r = \frac{3}{2}$ .	1
10675	Find $a_{7}$ of a geometric progression if $a_{1} = \frac{1}{9} and r = - 3$ .	1
10676	Find $a_{2} 6$ of a geometric progression if $a_{1} = \frac{1}{50} and r = 2$ .	1
10677	Find $a_{5}$ of a geometric progression if $a_{1} = 3 and r = \frac{4}{3}$ .	1
10678	Find $a_{1} 2$ of a geometric progression if $a_{1} = 7 and r = - 0.3333$ .	1
10679	Find $a_{1} 2$ of a geometric progression if $a_{1} = \frac{1}{8} and r = \frac{3}{4}$ .	1
10680	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{1}{10} and r = \frac{3}{2}$ .	1
10681	$a_{1} = 2, r = - 3, a_{1} = ?, r = ?$	1
10682	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{11}{100} and r = \frac{19}{2}$ .	1
10683	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{2} = 18 and a_{3} = 54$ .	1
10684	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = \frac{1}{9} and r = 3$ .	1
10685	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 1 and r = 3$ .	1
10686	Find $a_{1}$ of a geometric progression if $a_{1} = 3 and r = \frac{3}{7}$ .	1
10687	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 250 and r = - \frac{3}{5}$ .	1
10688	Find $a_{5}$ of a geometric progression if $a_{1} = 18 and r = \frac{5}{9}$ .	1
10689	Find $a_{1} 0$ of a geometric progression if $a_{1} = 18 and r = \frac{5}{9}$ .	1
10690	Find $a_{3} 0$ of a geometric progression if $a_{1} = 2 and r = 1$ .	1
10691	Find $a_{7}$ of a geometric progression if $a_{1} = 6 and r = 4$ .	1
10692	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = \frac{1}{4}$ .	1
10693	Find first element ( $a_{1}$ ) and a common ration ( $r$ ) of a geometic progression if $a_{8} = \frac{2}{3} and a_{5} = 18$ .	1
10694	Find $a_{2} 5$ of a geometric progression if $a_{1} = 6 and r = 2$ .	1
10695	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 729 and r = \frac{1}{3}$ .	1
10696	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 729 and r = \frac{1}{3}$ .	1
10697	Find $a_{6}$ of a geometric progression if $a_{1} = 1 and r = \frac{11}{10}$ .	1
10698	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{11}{10}$ .	1
10699	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 15 and r = - 14$ .	1
10700	Find $a_{4}$ of a geometric progression if $a_{1} = - 3 and r = - 5$ .	1