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
51	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 3 and r = 2$ .	25
52	Find $a_{9}$ of a geometric progression if $a_{1} = 5 and r = 4$ .	25
53	Find $a_{1} 4$ of a geometric progression if $a_{1} = 10 and r = 2$ .	25
54	Find $a_{5}$ of a geometric progression if $a_{1} = 3 and r = 4$ .	25
55	Find $a_{8}$ of a geometric progression if $a_{1} = 3 and r = 3$ .	24
56	Find $a_{6}$ of a geometric progression if $a_{1} = 3 and r = - 4$ .	24
57	Find $a_{7}$ of a geometric progression if $a_{1} = 5 and r = 2$ .	24
58	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 2 and r = 3$ .	24
59	Find $a_{1} 2$ of a geometric progression if $a_{1} = 2 and r = 5$ .	23
60	Find $a_{5}$ of a geometric progression if $a_{1} = 2 and r = 2$ .	23
61	Find $a_{7}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	23
62	Find $a_{6}$ of a geometric progression if $a_{1} = 2 and r = 4$ .	23
63	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = 3$ .	23
64	Find $a_{5}$ of a geometric progression if $a_{1} = 243 and r = \frac{1}{3}$ .	23
65	Find $a_{5}$ of a geometric progression if $a_{1} = 3 and r = 3$ .	23
66	Find $a_{5}$ of a geometric progression if $a_{1} = 6 and r = 3$ .	22
67	Find $a_{8}$ of a geometric progression if $a_{1} = 2 and r = - 2$ .	22
68	Find $a_{7}$ of a geometric progression if $a_{1} = 2 and r = 4$ .	22
69	Find the sum of the first $7$ terms of a geometric sequence if $a_{1} = 3 and r = 2$ .	22
70	Find $a_{9}$ of a geometric progression if $a_{1} = 9 and r = 3$ .	22
71	Find $a_{1} 1$ of a geometric progression if $a_{1} = 5 and r = 4$ .	22
72	Find $a_{1} 1$ of a geometric progression if $a_{1} = 1 and r = 3$ .	22
73	Find $a_{7}$ of a geometric progression if $a_{1} = 1 and r = 5$ .	21
74	Find $a_{5}$ of a geometric progression if $a_{1} = 4 and r = 2$ .	21
75	Find $a_{8}$ of a geometric progression if $a_{1} = 5 and r = - 3$ .	21
76	Find the sum of the first $20$ terms of a geometric sequence if $a_{1} = 1 and r = - 1$ .	21
77	Find $a_{8}$ of a geometric progression if $a_{1} = 3 and r = 5$ .	21
78	Find $a_{7}$ of a geometric progression if $a_{1} = - 4 and r = 2$ .	21
79	Find $a_{7}$ of a geometric progression if $a_{1} = 3 and r = 3$ .	21
80	Find $a_{1} 0$ of a geometric progression if $a_{1} = \frac{2}{3} and r = \frac{3}{4}$ .	20
81	Find $a_{1} 0$ of a geometric progression if $a_{1} = 2 and r = 4$ .	20
82	Find $a_{6}$ of a geometric progression if $a_{1} = 5 and r = 4$ .	20
83	Find $a_{5}$ of a geometric progression if $a_{1} = 2 and r = 4$ .	20
84	Find $a_{1} 3$ of a geometric progression if $a_{1} = 5 and r = 2$ .	20
85	Find $a_{6}$ of a geometric progression if $a_{1} = 1 and r = 2$ .	20
86	Find $a_{1} 2$ of a geometric progression if $a_{1} = 3 and r = - 4$ .	20
87	Find $a_{6}$ of a geometric progression if $a_{1} = 100 and r = 2$ .	19
88	Find $a_{6}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	19
89	Find $a_{1} 0$ of a geometric progression if $a_{1} = 6 and r = - 4$ .	19
90	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 3 and r = 3$ .	19
91	Find $a_{4}$ of a geometric progression if $a_{1} = 2 and r = 3$ .	19
92	Find $a_{2} 4$ of a geometric progression if $a_{1} = 10 and r = 2$ .	19
93	Find $a_{4}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	18
94	Find $a_{2} 0$ of a geometric progression if $a_{1} = 1 and r = 2$ .	18
95	Find the sum of the first $5$ terms of a geometric sequence if $a_{1} = 3 and r = 4$ .	18
96	Find $a_{4}$ of a geometric progression if $a_{1} = 2 and r = 4$ .	18
97	Find the sum of the first $10$ terms of a geometric sequence if $a_{1} = 6 and r = 2$ .	18
98	Find $a_{1} 0$ of a geometric progression if $a_{1} = 5 and r = 2$ .	18
99	Find $a_{9}$ of a geometric progression if $a_{1} = 3 and r = 2$ .	18
100	Find $a_{1} 2$ of a geometric progression if $a_{1} = 2 and r = 3$ .	18