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
3151	Find $ a_12 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 3 $.	3
3152	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3153	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 16 }{ 9 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
3154	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	3
3155	Find $ a_7 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
3156	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	3
3157	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 9 } ~~ \text{and} ~~ r = 3 $.	3
3158	Find $ a_7 $ of a geometric progression if $ a_1 = 30 ~~ \text{and} ~~ r = 24 $.	3
3159	Find $ a_2 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	3
3160	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 5 }{ 6 } $.	3
3161	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	3
3162	Find $ a_2 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	3
3163	$$ a_1 = 2 ~~,~~ r = 3 ~~,~~ a_1 = ? ~~,~~ r = ? $$	3
3164	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3165	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 10 } = 378 $.	3
3166	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 10 } = 378 $.	3
3167	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 9 } = 256 $.	3
3168	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 9 } = 256 $.	3
3169	Find the sum of the first $ 34 $ terms of a geometric sequence if $ a_1 = 60 ~~ \text{and} ~~ r = 0.89 $.	3
3170	Find $ a_5 $ of a geometric progression if $ a_1 = 224 ~~ \text{and} ~~ r = 2 $.	3
3171	Find $ a_9 $ of a geometric progression if $ a_1 = -65536 ~~ \text{and} ~~ r = 4 $.	3
3172	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	3
3173	$$ a_1 = 3 ~,~ r = 4 ~,~ a_n = 1023 ~,~ n = ? $$	3
3174	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $.	3
3175	Find $ a_2 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	3
3176	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	3
3177	Find $ a_7 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $.	3
3178	Find $ a_7 $ of a geometric progression if $ a_1 = -113 ~~ \text{and} ~~ r = 6 $.	3
3179	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.002 ~~ \text{and} ~~ r = 1.2 $.	3
3180	Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 1.2 $.	3
3181	Find the sum of the first $ 35 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 1.2 $.	3
3182	Find the sum of the first $ 35 $ terms of a geometric sequence if $ a_1 = 0.002 ~~ \text{and} ~~ r = 1.2 $.	3
3183	Find $ a_12 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
3184	Find $ a_12 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	3
3185	Find $ a_4 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 5 $.	3
3186	Find $ a_8 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -5 $.	3
3187	Find $ a_9 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -5 $.	3
3188	Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
3189	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 12 ~~ \text{and} ~~ a_{ 5 } = 48 $.	3
3190	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	3
3191	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	3
3192	Find the sum of the first $ 84 $ terms of a geometric sequence if $ a_1 = 7500 ~~ \text{and} ~~ r = 1.071 $.	3
3193	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
3194	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 10 $.	3
3195	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = -9 ~~ \text{and} ~~ r = -1 $.	3
3196	Find $ a_4 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = 4 $.	3
3197	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 2187 }{ 128 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
3198	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	3
3199	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = -4 $.	3
3200	Find $ a_8 $ of a geometric progression if $ a_1 = -4300 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 10 } $.	3