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
9851	Find $ a_5 $ of a geometric progression if $ a_1 = 105948 ~~ \text{and} ~~ r = 3 $.	1
9852	Find $ a_5 $ of a geometric progression if $ a_1 = 105948 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $.	1
9853	Find $ a_7 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 1.66 $.	1
9854	Find $ a_6 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9855	Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9856	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	1
9857	Find $ a_17 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	1
9858	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = 1.05 $.	1
9859	Find $ a_4 $ of a geometric progression if $ a_1 = -24 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 5 } $.	1
9860	Find $ a_2 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -4 $.	1
9861	Find $ a_3 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -4 $.	1
9862	Find $ a_5 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -4 $.	1
9863	Find $ a_6 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -4 $.	1
9864	Find $ a_9 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 4 $.	1
9865	Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	1
9866	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 8 } = 78 ~~ \text{and} ~~ a_{ 26 } = 240 $.	1
9867	Find $ a_1 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	1
9868	Find $ a_5 $ of a geometric progression if $ a_1 = 50000 ~~ \text{and} ~~ r = 4 $.	1
9869	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 20 } $.	1
9870	Find $ a_5 $ of a geometric progression if $ a_1 = 300 ~~ \text{and} ~~ r = 7 $.	1
9871	Find $ a_5 $ of a geometric progression if $ a_1 = 300 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 100 } $.	1
9872	Find $ a_60 $ of a geometric progression if $ a_1 = 300 ~~ \text{and} ~~ r = 0.07 $.	1
9873	Find $ a_3 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
9874	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
9875	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 8 }{ 15 } ~~ \text{and} ~~ r = \frac{ 8 }{ 15 } $.	1
9876	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 72 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9877	Find $ a_9 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
9878	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 0.22 $.	1
9879	Find the sum of the first $ 360 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 0.22 $.	1
9880	Find $ a_11 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	1
9881	Find the sum of the first $ 92 $ terms of a geometric sequence if $ a_1 = 400 ~~ \text{and} ~~ r = 1.02 $.	1
9882	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -\frac{ 3 }{ 4 } $.	1
9883	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 29 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	1
9884	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 25 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	1
9885	$$ a_1 = 7 ~,~ r = 3 ~,~ a_n = 137781 ~,~ n = ? $$	1
9886	$$ a_1 = 9 ~,~ r = 4 ~,~ a_n = 589824 ~,~ n = ? $$	1
9887	$$ a_1 = 3 ~,~ r = 5 ~,~ a_n = 1171875 ~,~ n = ? $$	1
9888	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	1
9889	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	1
9890	Find $ a_8 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 6 } $.	1
9891	Find $ a_10 $ of a geometric progression if $ a_1 = 1024 ~~ \text{and} ~~ r = 2 $.	1
9892	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 123 ~~ \text{and} ~~ r = 12 $.	1
9893	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 123 ~~ \text{and} ~~ r = 12 $.	1
9894	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 6 $.	1
9895	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9896	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9897	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 2.5 ~~ \text{and} ~~ r = 1.75 $.	1
9898	Find $ a_9 $ of a geometric progression if $ a_1 = 42 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 6 } $.	1
9899	Find $ a_10 $ of a geometric progression if $ a_1 = 42 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 6 } $.	1
9900	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	1