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
3051	Find $ a_9 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	3
3052	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	3
3053	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 4 $.	3
3054	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	3
3055	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	3
3056	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	3
3057	Find $ a_25 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	3
3058	Find the sum of the first $ 75 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.2 $.	3
3059	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.	3
3060	Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	3
3061	Find $ a_7 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	3
3062	Find $ a_8 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $.	3
3063	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	3
3064	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	3
3065	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
3066	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 48 ~~ \text{and} ~~ r = \frac{ 5 }{ 4 } $.	3
3067	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3068	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = -\frac{ 7 }{ 9 } $.	3
3069	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	3
3070	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -\frac{ 3 }{ 11 } $.	3
3071	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 147 ~~ \text{and} ~~ r = 1000 $.	3
3072	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	3
3073	Find $ a_1 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	3
3074	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 36000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	3
3075	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	3
3076	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 2 $.	3
3077	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 400 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	3
3078	Find the sum of the first $ 45 $ terms of a geometric sequence if $ a_1 = -0.5 ~~ \text{and} ~~ r = -3 $.	3
3079	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3080	Find $ a_5 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	3
3081	Find $ a_2 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	3
3082	Find $ a_3 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	3
3083	Find $ a_4 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	3
3084	Find $ a_6 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	3
3085	Find $ a_9 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 5 $.	3
3086	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 7 $.	3
3087	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	3
3088	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 0.09877 ~~ \text{and} ~~ r = 0.1975 $.	3
3089	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 8 $.	3
3090	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $.	3
3091	Find $ a_6 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = 8 $.	3
3092	Find the sum of the first $ 29 $ terms of a geometric sequence if $ a_1 = 171000 ~~ \text{and} ~~ r = 1.33 $.	3
3093	Find $ a_8 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	3
3094	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	3
3095	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	3
3096	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	3
3097	Find $ a_4 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	3
3098	Find $ a_15 $ of a geometric progression if $ a_1 = 6144 ~~ \text{and} ~~ r = 2 $.	3
3099	Find $ a_8 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 5 $.	3
3100	Find the sum of the first $ 90 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = 0.03 $.	3