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
10351	Find $ a_10 $ of a geometric progression if $ a_1 = 39366 ~~ \text{and} ~~ r = 3 $.	1
10352	Find the sum of the first $ 14 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 5 $.	1
10353	$$ a_1 = 810 ~,~ r = \frac{ 5 }{ 3 } ~,~ a_n = 7 ~,~ n = ? $$	1
10354	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 810 ~~ \text{and} ~~ a_{ 7 } = \frac{ 156250 }{ 9 } $.	1
10355	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
10356	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -64 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
10357	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 1.22 $.	1
10358	Find $ a_13 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	1
10359	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $.	1
10360	Find $ a_18 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	1
10361	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	1
10362	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 5 $.	1
10363	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = \frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 4 } = \frac{ 2 }{ 9 } $.	1
10364	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 9 }{ 20 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
10365	Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 13 }{ 10 } $.	1
10366	Find $ a_18 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
10367	Find $ a_18 $ of a geometric progression if $ a_1 = 900 ~~ \text{and} ~~ r = 0.3 $.	1
10368	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 27500 ~~ \text{and} ~~ r = 1.025 $.	1
10369	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 27500 ~~ \text{and} ~~ r = 1.066 $.	1
10370	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 18000 ~~ \text{and} ~~ r = 1.066 $.	1
10371	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -\frac{ 3 }{ 2 } ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
10372	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
10373	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ r = \frac{ 5 }{ 6 } $.	1
10374	Find the sum of the first $ 37 $ terms of a geometric sequence if $ a_1 = 1000 ~~ \text{and} ~~ r = 320000 $.	1
10375	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
10376	Find $ a_30 $ of a geometric progression if $ a_1 = 0.01 ~~ \text{and} ~~ r = 1.01 $.	1
10377	Find $ a_30 $ of a geometric progression if $ a_1 = 1.01 ~~ \text{and} ~~ r = 1.01 $.	1
10378	Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	1
10379	Find the sum of the first $ 7305 $ terms of a geometric sequence if $ a_1 = 0.01 ~~ \text{and} ~~ r = 2 $.	1
10380	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	1
10381	Find the sum of the first $ 200 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 21 }{ 20 } $.	1
10382	Find $ a_7 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
10383	Find $ a_300 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	1
10384	Find $ a_400 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	1
10385	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 2 $.	1
10386	Find $ a_4 $ of a geometric progression if $ a_1 = 768 ~~ \text{and} ~~ r = -12 $.	1
10387	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $.	1
10388	Find $ a_30 $ of a geometric progression if $ a_1 = 2500 ~~ \text{and} ~~ r = 0.994 $.	1
10389	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 8 } ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1
10390	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 8 } ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	1
10391	$$ a_1 = 4 ~,~ r = 5 ~,~ S_n = 15624 ~,~ n = ? $$	1
10392	Find $ a_5 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 7 $.	1
10393	Find $ a_5 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 2 $.	1
10394	Find $ a_5 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 1 $.	1
10395	$$ a_1 = 40 ~,~ r = \frac{ 1 }{ 2 } ~,~ a_n = 10 ~,~ n = ? $$	1
10396	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	1
10397	Find the sum of the first $ 21 $ terms of a geometric sequence if $ a_1 = 54000 ~~ \text{and} ~~ r = 1.05 $.	1
10398	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 4 } = 260 $.	1
10399	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 16 }{ 5 } $.	1
10400	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 3000 ~~ \text{and} ~~ r = 10 $.	1