Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

Select category

ID	Problem	Count
10351	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 4 and r = - 2$ .	1
10352	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 46 and r = - \frac{1}{2}$ .	1
10353	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 46 and r = \frac{1}{2}$ .	1
10354	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 46 and r = \frac{1}{2}$ .	1
10355	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 46 and r = - \frac{3}{2}$ .	1
10356	$a_{1} = 46, r = \frac{1}{2}, a_{1} = ?, r = ?$	1
10357	Find $a_{4}$ of a geometric progression if $a_{1} = 4 and r = - 1$ .	1
10358	Find $a_{8}$ of a geometric progression if $a_{1} = 3 and r = 1$ .	1
10359	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10360	Find $a_{4}$ of a geometric progression if $a_{1} = 1 and r = \frac{1}{2}$ .	1
10361	Find the sum of the first $42$ terms of a geometric sequence if $a_{1} = 20000 and r = 1.1$ .	1
10362	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = 2 and r = 4$ .	1
10363	Find $a_{2}$ of a geometric progression if $a_{1} = \frac{1}{49} and r = - 7$ .	1
10364	Find $a_{1} 00$ of a geometric progression if $a_{1} = 49 and r = 1$ .	1
10365	Find $a_{7}$ of a geometric progression if $a_{1} = - 2 and r = 6$ .	1
10366	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = - 2 and r = 6$ .	1
10367	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = - 4 and r = 6$ .	1
10368	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 0 and r = 2$ .	1
10369	Find $a_{1} 5$ of a geometric progression if $a_{1} = 0 and r = 2$ .	1
10370	Find the sum of the first $9$ terms of a geometric sequence if $a_{1} = \frac{1}{2} and r = \frac{1}{2}$ .	1
10371	$a_{1} = 4, r = 5, S_{n} = 78124, n = ?$	1
10372	Find $a_{1}$ of a geometric progression if $a_{1} = 4 and r = 3$ .	1
10373	Find the sum of the first $99999999$ terms of a geometric sequence if $a_{1} = - 4.2 and r = - \frac{1}{5}$ .	1
10374	Find the sum of the first $9223372036854775807$ terms of a geometric sequence if $a_{1} = - 4.2 and r = - \frac{1}{5}$ .	1
10375	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 1 and r = 3$ .	1
10376	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = - 1 and r = 6$ .	1
10377	Find $a_{2}$ of a geometric progression if $a_{1} = 1000 and r = 1$ .	1
10378	Find $a_{4}$ of a geometric progression if $a_{1} = 3 and r = 4$ .	1
10379	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 12 and r = \frac{1}{4}$ .	1
10380	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 5 and r = \frac{4}{3}$ .	1
10381	Find $a_{1} 0$ of a geometric progression if $a_{1} = 48 and r = \frac{1}{4}$ .	1
10382	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 48 and r = \frac{1}{4}$ .	1
10383	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 50 and r = 0.15$ .	1
10384	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 50 and r = 15$ .	1
10385	Find the sum of the first $8$ terms of a geometric sequence if $a_{1} = 50 and r = 1.15$ .	1
10386	Find $a_{4}$ of a geometric progression if $a_{1} = 5 and r = \frac{5}{4}$ .	1
10387	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 4 and r = 4$ .	1
10388	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 16 and r = - 4$ .	1
10389	Find the sum of the first $13$ terms of a geometric sequence if $a_{1} = - \frac{9}{2} and r = - \frac{3}{2}$ .	1
10390	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = 4$ .	1
10391	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = - 3$ .	1
10392	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = - 2 and r = - 3$ .	1
10393	$a_{1} = 432, r = 0.1667, a_{1} = ?, r = ?$	1
10394	Find $a_{4}$ of a geometric progression if $a_{1} = 64 and r = 1.333$ .	1
10395	Find $a_{4}$ of a geometric progression if $a_{1} = 64 and r = 1.333$ .	1
10396	Find common ratio ( $r$ ) in geometic progression if $a_{1} = \frac{182}{5} and a_{3} = 13.1$ .	1
10397	Find $a_{1} 1$ of a geometric progression if $a_{1} = \frac{32}{9} and r = - \frac{2}{3}$ .	1
10398	Find $a_{2} 4$ of a geometric progression if $a_{1} = 2 and r = 2$ .	1
10399	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 500 and r = 0.8$ .	1
10400	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