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
3201	Find $ a_11 $ of a geometric progression if $ a_1 = -512 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	3
3202	Find $ a_7 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -5 $.	3
3203	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	3
3204	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	3
3205	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.1275 ~~ \text{and} ~~ r = 86 $.	3
3206	Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 8 $.	3
3207	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2048 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	3
3208	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	3
3209	Find $ a_12 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -3 $.	3
3210	Find $ a_3 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 4 $.	3
3211	Find $ a_4 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 4 $.	3
3212	Find $ a_4 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 3 $.	3
3213	Find $ a_3 $ of a geometric progression if $ a_1 = 11 ~~ \text{and} ~~ r = 4 $.	3
3214	$$ a_1 = 8 ~,~ r = 3 ~,~ a_n = 52488 ~,~ n = ? $$	3
3215	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -5 $.	3
3216	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 200000 ~~ \text{and} ~~ r = 0.94 $.	3
3217	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 16 } ~~ \text{and} ~~ r = 2 $.	3
3218	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.	3
3219	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 8 $.	3
3220	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	3
3221	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = -4 $.	3
3222	$$ a_1 = \frac{ 3 }{ 5 } ~,~ r = 2 ~,~ a_n = 1536 ~,~ n = ? $$	3
3223	Find $ a_11 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	3
3224	Find the sum of the first $ 200 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 0.999 $.	3
3225	Find the sum of the first $ 300 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 0.999 $.	3
3226	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 0.001 ~~ \text{and} ~~ r = 0.999 $.	3
3227	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	3
3228	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	3
3229	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	3
3230	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 35000 ~~ \text{and} ~~ r = 0.06 $.	3
3231	Find $ a_20 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 0.25 $.	3
3232	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -2 $.	3
3233	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	3
3234	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = 2 $.	3
3235	Find $ a_11 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	3
3236	Find $ a_1 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 8 }{ 5 } $.	3
3237	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3238	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3239	Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	3
3240	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $.	3
3241	Find $ a_5 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -3 $.	3
3242	Find $ a_10 $ of a geometric progression if $ a_1 = 6750 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	3
3243	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3244	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 600 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3245	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	3
3246	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 9 ~~ \text{and} ~~ a_{ 3 } = 81 $.	3
3247	Find $ a_5 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 10 } $.	3
3248	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	3
3249	Find $ a_7 $ of a geometric progression if $ a_1 = 36 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	3
3250	$$ a_1 = \frac{ 37 }{ 1048576 } ~,~ r = 4 ~,~ a_n = 15 ~,~ n = ? $$	3