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
101	Find $ a_8 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	20
102	Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	20
103	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $.	20
104	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	20
105	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	20
106	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	19
107	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	19
108	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	19
109	Find $ a_20 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	19
110	Find $ a_8 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	19
111	Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	19
112	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	19
113	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	19
114	Find $ a_24 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	19
115	Find $ a_15 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	19
116	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	19
117	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	18
118	Find $ a_30 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	18
119	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	18
120	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	18
121	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	18
122	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	18
123	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	18
124	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 4 $.	18
125	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	18
126	Find $ a_5 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -2 $.	18
127	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	18
128	Find $ a_12 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	17
129	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	17
130	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	17
131	Find $ a_20 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -1 $.	17
132	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	17
133	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	17
134	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	17
135	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 729 ~~ \text{and} ~~ r = -3 $.	17
136	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	17
137	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	17
138	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	17
139	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	16
140	Find $ a_13 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -5 $.	16
141	Find $ a_6 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	16
142	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	16
143	Find $ a_8 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	16
144	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	16
145	Find $ a_15 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	16
146	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	16
147	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	16
148	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	16
149	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	16
150	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $.	16