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
3101	Find $ a_5 $ of a geometric progression if $ a_1 = 2000 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	3
3102	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.95 $.	3
3103	Find $ a_5 $ of a geometric progression if $ a_1 = 108 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 18 } $.	3
3104	Find $ a_5 $ of a geometric progression if $ a_1 = -6 ~~ \text{and} ~~ r = 7 $.	3
3105	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	3
3106	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 5 } ~~ \text{and} ~~ r = -\dfrac{ 9 }{ 25 } $.	3
3107	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	3
3108	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	3
3109	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 72 ~~ \text{and} ~~ r = 6 $.	3
3110	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	3
3111	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -4 $.	3
3112	Find $ a_10 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -1 $.	3
3113	Find $ a_10 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -4 $.	3
3114	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = \frac{ 4 }{ 3 } ~~ \text{and} ~~ r = 3 $.	3
3115	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 16 } ~~ \text{and} ~~ r = -2 $.	3
3116	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
3117	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	3
3118	Find $ a_2 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 7 } $.	3
3119	Find $ a_3 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
3120	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 7 $.	3
3121	Find $ a_11 $ of a geometric progression if $ a_1 = 64 ~~ \text{and} ~~ r = 0.5 $.	3
3122	Find $ a_6 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	3
3123	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	3
3124	Find $ a_7 $ of a geometric progression if $ a_1 = 0.004 ~~ \text{and} ~~ r = 10 $.	3
3125	Find $ a_20 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -1 $.	3
3126	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 1.08 $.	3
3127	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 8 $.	3
3128	Find $ a_25 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	3
3129	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 54 ~~ \text{and} ~~ r = 3 $.	3
3130	Find $ a_9 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $.	3
3131	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	3
3132	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	3
3133	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 703 }{ 100 } ~~ \text{and} ~~ r = -5 $.	3
3134	Find $ a_6 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 4 } $.	3
3135	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	3
3136	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	3
3137	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $.	3
3138	Find $ a_6 $ of a geometric progression if $ a_1 = -10 ~~ \text{and} ~~ r = 2 $.	3
3139	Find $ a_300 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 0.002 $.	3
3140	Find $ a_4 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	3
3141	Find $ a_4 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 2 } $.	3
3142	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -\frac{ 5 }{ 2 } $.	3
3143	Find $ a_12 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 5 $.	3
3144	Find $ a_12 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	3
3145	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -5 $.	3
3146	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -12 ~~ \text{and} ~~ r = -3 $.	3
3147	Find $ a_3 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	3
3148	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3149	Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -2 $.	3
3150	Find $ a_6 $ of a geometric progression if $ a_1 = -12 ~~ \text{and} ~~ r = -2 $.	3