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
8351	Find $ a_10 $ of a geometric progression if $ a_1 = 1.414 ~~ \text{and} ~~ r = -1.414 $.	1
8352	Find $ a_6 $ of a geometric progression if $ a_1 = -125 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
8353	Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	1
8354	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 5 } ~~ \text{and} ~~ r = 0.5774 $.	1
8355	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = -3 $.	1
8356	Find $ a_12 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
8357	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
8358	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
8359	Find $ a_20 $ of a geometric progression if $ a_1 = 486 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8360	Find $ a_7 $ of a geometric progression if $ a_1 = 486 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8361	Find $ a_8 $ of a geometric progression if $ a_1 = 13122 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8362	Find $ a_16 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.139 $.	1
8363	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.139 $.	1
8364	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 6 } = 25 ~~ \text{and} ~~ a_{ 8 } = 4 $.	1
8365	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 1 }{ 5 } ~~ \text{and} ~~ a_{ 6 } = \frac{ 8 }{ 25 } $.	1
8366	Find the sum of the first $ 22 $ terms of a geometric sequence if $ a_1 = 15625 ~~ \text{and} ~~ r = 5 $.	1
8367	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 51 }{ 50 } $.	1
8368	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 51 }{ 50 } $.	1
8369	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.	1
8370	Find $ a_6 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 51 }{ 50 } $.	1
8371	Find $ a_6 $ of a geometric progression if $ a_1 = 7640 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	1
8372	Find $ a_4 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8373	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 10 } $.	1
8374	Find $ a_12 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	1
8375	Find $ a_5 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 5 $.	1
8376	Find the sum of the first $ 25 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -2 $.	1
8377	Find $ a_7 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 5 $.	1
8378	Find $ a_9 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
8379	Find $ a_25 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = 1.025 $.	1
8380	Find $ a_70 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = 0.95 $.	1
8381	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1.477 ~~ \text{and} ~~ r = 0.907 $.	1
8382	Find $ a_5 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	1
8383	Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.	1
8384	Find $ a_4 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 9 $.	1
8385	Find $ a_10 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
8386	Find the sum of the first $ 80 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	1
8387	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 7 } $.	1
8388	Find $ a_100 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	1
8389	Find $ a_10 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	1
8390	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 6 } $.	1
8391	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = 3 $.	1
8392	Find $ a_15 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -9 $.	1
8393	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 5 ~~ \text{and} ~~ a_{ 15 } = 4350 $.	1
8394	Find $ a_6 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	1
8395	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	1
8396	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 0.17 $.	1
8397	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -\frac{ 1 }{ 2 } $.	1
8398	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 4 $.	1
8399	$$ a_1 = 3 ~,~ r = 4 ~,~ S_n = 4095 ~,~ n = ? $$	1
8400	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1