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
11001	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = 0.9259$ .	1
11002	Find the sum of the first $1000000000011110$ terms of a geometric sequence if $a_{1} = \frac{1}{4} and r = \frac{1}{4}$ .	1
11003	Find $a_{4}$ of a geometric progression if $a_{1} = \frac{14}{3} and r = \frac{14}{3}$ .	1
11004	Find $a_{2} 0$ of a geometric progression if $a_{1} = \frac{3}{8} and r = 1$ .	1
11005	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = - \frac{3}{8}$ .	1
11006	Find $a_{2} 5$ of a geometric progression if $a_{1} = 100 and r = 2$ .	1
11007	Find $a_{1} 03$ of a geometric progression if $a_{1} = 1 and r = 2$ .	1
11008	Find the sum of the first $265$ terms of a geometric sequence if $a_{1} = 121 and r = 1.15$ .	1
11009	Find the sum of the first $164$ terms of a geometric sequence if $a_{1} = 160 and r = 1.15$ .	1
11010	Find $a_{4}$ of a geometric progression if $a_{1} = - 16 and r = - \frac{1}{2}$ .	1
11011	Find the sum of the first $10000$ terms of a geometric sequence if $a_{1} = 1 and r = 0.75$ .	1
11012	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{10}{7}$ .	1
11013	Find $a_{1} 0$ of a geometric progression if $a_{1} = 1 and r = \frac{3}{10}$ .	1
11014	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{5}$ .	1
11015	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = \frac{1}{4}$ .	1
11016	Find $a_{1} 5$ of a geometric progression if $a_{1} = 15 and r = 1.5$ .	1
11017	Find $a_{1} 3$ of a geometric progression if $a_{1} = 15 and r = 1.5$ .	1
11018	Find $a_{1} 2$ of a geometric progression if $a_{1} = 15 and r = 1.5$ .	1
11019	Find $a_{1} 2$ of a geometric progression if $a_{1} = 10 and r = 1.5$ .	1
11020	Find $a_{8}$ of a geometric progression if $a_{1} = 75 and r = 1.5$ .	1
11021	Find $a_{9}$ of a geometric progression if $a_{1} = 25 and r = 1.5$ .	1
11022	Find $a_{1} 0$ of a geometric progression if $a_{1} = 25 and r = 1.5$ .	1
11023	Find $a_{7}$ of a geometric progression if $a_{1} = 10 and r = 2.5$ .	1
11024	Find $a_{6}$ of a geometric progression if $a_{1} = - 2 and r = 12$ .	1
11025	Find the sum of the first $3$ terms of a geometric sequence if $a_{1} = 56 and r = 43$ .	1
11026	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 1 and r = 0.05$ .	1
11027	Find the sum of the first $100$ terms of a geometric sequence if $a_{1} = - \frac{1}{3} and r = - \frac{1}{3}$ .	1
11028	Find the sum of the first $12$ terms of a geometric sequence if $a_{1} = - 3 and r = - 2$ .	1
11029	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = 1 and r = 12$ .	1
11030	Find the sum of the first $6$ terms of a geometric sequence if $a_{1} = - 3 and r = - 4$ .	1
11031	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{1}{3} and r = 3$ .	1
11032	Find the sum of the first $4$ terms of a geometric sequence if $a_{1} = 108 and r = - \frac{2}{3}$ .	1
11033	Find $a_{1} 0$ of a geometric progression if $a_{1} = 4 and r = - \frac{1}{2}$ .	1
11034	Find $a_{5}$ of a geometric progression if $a_{1} = 81 and r = 5$ .	1
11035	Find $a_{5}$ of a geometric progression if $a_{1} = 8 and r = \frac{4}{5}$ .	1
11036	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 8 and r = \frac{4}{5}$ .	1
11037	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = \frac{5}{4} and r = \frac{1}{4}$ .	1
11038	Find the sum of the first $15$ terms of a geometric sequence if $a_{1} = 3 and r = - \frac{2}{3}$ .	1
11039	Find the sum of the first $9223372036854775807$ terms of a geometric sequence if $a_{1} = 4 and r = - \frac{1}{3}$ .	1
11040	Find $a_{1} 0$ of a geometric progression if $a_{1} = 10 and r = 1.22$ .	1
11041	Find $a_{3} 0$ of a geometric progression if $a_{1} = 1 and r = 2$ .	1
11042	Find $a_{7}$ of a geometric progression if $a_{1} = 10 and r = 2$ .	1
11043	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 7 and r = \frac{3}{4}$ .	1
11044	Find $a_{4} 8$ of a geometric progression if $a_{1} = 1.006 and r = 0.005833$ .	1
11045	Find the sum of the first $48$ terms of a geometric sequence if $a_{1} = 1.006 and r = 1.006$ .	1
11046	Find $a_{5}$ of a geometric progression if $a_{1} = \frac{176}{5} and r = \frac{5}{4}$ .	1
11047	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = \frac{176}{5} and r = \frac{5}{4}$ .	1
11048	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 80 and a_{4} = 10$ .	1
11049	Find common ratio ( $r$ ) in geometic progression if $a_{1} = 2 and a_{5} = \frac{13}{8}$ .	1
11050	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = \frac{1}{5} and r = \frac{1}{2}$ .	1