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
10451	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 5000 and r = 1.025$ .	1
10452	Find the sum of the first $30$ terms of a geometric sequence if $a_{1} = 4000 and r = 1.045$ .	1
10453	Find the sum of the first $1$ terms of a geometric sequence if $a_{1} = \frac{3}{2} and r = 10$ .	1
10454	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = - 3 and r = - \frac{1}{3}$ .	1
10455	Find $a_{5}$ of a geometric progression if $a_{1} = 5 and r = 7$ .	1
10456	Find $a_{9}$ of a geometric progression if $a_{1} = - 32 and r = - \frac{1}{2}$ .	1
10457	Find $a_{5}$ of a geometric progression if $a_{1} = - 8 and r = - \frac{5}{4}$ .	1
10458	Find $a_{4}$ of a geometric progression if $a_{1} = - 11 and r = 6$ .	1
10459	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = - 4$ .	1
10460	Find $a_{9}$ of a geometric progression if $a_{1} = - 8 and r = - 2$ .	1
10461	Find $a_{1} 0$ of a geometric progression if $a_{1} = - 18 and r = - 3$ .	1
10462	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = - 2$ .	1
10463	$a_{1} = 128, r = \frac{1}{2}, a_{n} = 1, n = ?$	1
10464	Find $a_{1}$ of a geometric progression if $a_{1} = 24 and r = \frac{1}{2}$ .	1
10465	Find $a_{2}$ of a geometric progression if $a_{1} = 24 and r = \frac{1}{2}$ .	1
10466	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 3 and r = 10$ .	1
10467	Find $a_{1} 0$ of a geometric progression if $a_{1} = 72 and r = - \frac{3}{2}$ .	1
10468	Find $a_{7}$ of a geometric progression if $a_{1} = - 4 and r = - 2$ .	1
10469	Find $a_{3}$ of a geometric progression if $a_{1} = 72 and r = \frac{1}{6}$ .	1
10470	Find $a_{5}$ of a geometric progression if $a_{1} = 72 and r = 16$ .	1
10471	Find $a_{6}$ of a geometric progression if $a_{1} = 72 and r = \frac{1}{6}$ .	1
10472	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 9 and r = 5$ .	1
10473	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 15 and r = - 2$ .	1
10474	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 12 and r = - 1$ .	1
10475	Find $a_{2}$ of a geometric progression if $a_{1} = - 192 and r = 6$ .	1
10476	Find $a_{2}$ of a geometric progression if $a_{1} = - 192 and r = 4$ .	1
10477	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 10 and r = 10$ .	1
10478	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = 10$ .	1
10479	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = 1$ .	1
10480	Find $a_{1}$ of a geometric progression if $a_{1} = 10 and r = 3$ .	1
10481	Find $a_{1}$ of a geometric progression if $a_{1} = 10 and r = - 3$ .	1
10482	Find $a_{1}$ of a geometric progression if $a_{1} = - 3 and r = - 3$ .	1
10483	Find first element ( $a_{1}$ ) of a geometic progression if $r = - 3 and a_{5} = 162$ .	1
10484	Find $a_{3}$ of a geometric progression if $a_{1} = - 118096 and r = 1$ .	1
10485	Find $a_{8}$ of a geometric progression if $a_{1} = 118096 and r = - 3$ .	1
10486	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10487	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{1}{10} and r = \frac{1}{10}$ .	1
10488	Find $a_{3}$ of a geometric progression if $a_{1} = 3 and r = - 3$ .	1
10489	Find $a_{6}$ of a geometric progression if $a_{1} = 3 and r = - 3$ .	1
10490	Find $a_{2}$ of a geometric progression if $a_{1} = 3 and r = - 3$ .	1
10491	$a_{1} = 3, r = - 3, a_{1} = ?, r = ?$	1
10492	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = - 4 and r = - 4$ .	1
10493	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = - 3 and r = - 2$ .	1
10494	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = - 3 and r = - 2$ .	1
10495	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{1}{2} and r = 1$ .	1
10496	Find the sum of the first $2$ terms of a geometric sequence if $a_{1} = 1000 and r = \frac{3}{4}$ .	1
10497	Find $a_{2}$ of a geometric progression if $a_{1} = 98 and r = \frac{1}{7}$ .	1
10498	Find $a_{6}$ of a geometric progression if $a_{1} = 3 and r = - 1$ .	1
10499	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 8 and r = - \frac{3}{4}$ .	1
10500	Find the sum of the first $17$ terms of a geometric sequence if $a_{1} = 128 and r = \frac{1}{2}$ .	1