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
6651	Find $ a_16 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -4 $.	1
6652	Find $ a_7 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
6653	Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 5 } $.	1
6654	Find $ a_13 $ of a geometric progression if $ a_1 = 3750 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
6655	Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -6 $.	1
6656	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1
6657	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
6658	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
6659	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	1
6660	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 25 $.	1
6661	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 8 $.	1
6662	$$ a_1 = 4 ~,~ r = 3 ~,~ a_n = 3 ~,~ n = ? $$	1
6663	Find $ a_2 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	1
6664	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
6665	Find $ a_6 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	1
6666	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	1
6667	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 240 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	1
6668	Find $ a_14 $ of a geometric progression if $ a_1 = 160000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6669	Find $ a_6 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = 32 $.	1
6670	Find $ a_2 $ of a geometric progression if $ a_1 = 200000 ~~ \text{and} ~~ r = 1.09 $.	1
6671	Find $ a_50 $ of a geometric progression if $ a_1 = 200000 ~~ \text{and} ~~ r = 1.09 $.	1
6672	Find $ a_11 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2.33 $.	1
6673	Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6674	Find $ a_12 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6675	Find $ a_14 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	1
6676	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 1 } = \frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 2 }{ 9 } $.	1
6677	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 3 $.	1
6678	Find $ a_10 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	1
6679	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 50 } ~~ \text{and} ~~ r = 2 $.	1
6680	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -3 $.	1
6681	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 162 ~~ \text{and} ~~ r = 3 $.	1
6682	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ r = -3 $.	1
6683	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 2560 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
6684	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
6685	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 0.05 ~~ \text{and} ~~ r = 2 $.	1
6686	Find $ a_15 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	1
6687	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 55580 ~~ \text{and} ~~ r = 1.039 $.	1
6688	Find $ a_2 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 59 }{ 221 } $.	1
6689	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 32768 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
6690	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 729 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
6691	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
6692	Find $ a_4 $ of a geometric progression if $ a_1 = -128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
6693	Find $ a_7 $ of a geometric progression if $ a_1 = 270 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
6694	Find the sum of the first $ 26 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	1
6695	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 0.2 ~~ \text{and} ~~ r = 2 $.	1
6696	Find $ a_3 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	1
6697	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	1
6698	Find $ a_4 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 9 } $.	1
6699	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
6700	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $.	1