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
3351	Find $ a_1 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = -2 $.	2
3352	Find $ a_11 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3353	$$ a_1 = 1 ~,~ r = 4 ~,~ a_n = 12 ~,~ n = ? $$	2
3354	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 12 ~~ \text{and} ~~ a_{ 5 } = \frac{ 16 }{ 3 } $.	2
3355	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
3356	Find $ a_10 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3357	Find $ a_11 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 5 } ~~ \text{and} ~~ r = 3 $.	2
3358	Find $ a_15 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -4 $.	2
3359	Find $ a_7 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = -8 $.	2
3360	Find $ a_6 $ of a geometric progression if $ a_1 = -\dfrac{ 5 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3361	Find $ a_12 $ of a geometric progression if $ a_1 = 23 ~~ \text{and} ~~ r = -3 $.	2
3362	$$ a_1 = \frac{ 1 }{ 64 } ~~,~~ r = -2 ~~,~~ a_1 = ? ~~,~~ r = ? $$	2
3363	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1 }{ 64 } ~~ \text{and} ~~ a_{ 3 } = \frac{ 1 }{ 16 } $.	2
3364	Find $ a_2 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	2
3365	Find $ a_18 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	2
3366	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = 3 $.	2
3367	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 24 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3368	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	2
3369	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 1295 ~~ \text{and} ~~ r = 6 $.	2
3370	Find $ a_100 $ of a geometric progression if $ a_1 = 0.5 ~~ \text{and} ~~ r = 0.5 $.	2
3371	Find the sum of the first $ 37 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	2
3372	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 300 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3373	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 7 }{ 10 } $.	2
3374	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 4 } = 51200 ~~ \text{and} ~~ a_{ 7 } = \frac{ 131072 }{ 5 } $.	2
3375	Find $ a_10 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	2
3376	Find $ a_10 $ of a geometric progression if $ a_1 = 22 ~~ \text{and} ~~ r = 3 $.	2
3377	Find $ a_10 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = -4 $.	2
3378	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -5 $.	2
3379	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 7 $.	2
3380	Find $ a_6 $ of a geometric progression if $ a_1 = 7680 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
3381	Find $ a_3 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.	2
3382	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 8 } ~~ \text{and} ~~ r = -4 $.	2
3383	Find $ a_79 $ of a geometric progression if $ a_1 = \dfrac{ 99 }{ 100 } ~~ \text{and} ~~ r = 1 $.	2
3384	Find $ a_45 $ of a geometric progression if $ a_1 = -\dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = 1 $.	2
3385	Find the sum of the first $ 45 $ terms of a geometric sequence if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ r = 1 $.	2
3386	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 10 } $.	2
3387	Find $ a_7 $ of a geometric progression if $ a_1 = 6561 ~~ \text{and} ~~ r = -3 $.	2
3388	Find $ a_7 $ of a geometric progression if $ a_1 = 6561 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 10 } $.	2
3389	Find $ a_5 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = -5 $.	2
3390	Find $ a_5 $ of a geometric progression if $ a_1 = -3 ~~ \text{and} ~~ r = 2 $.	2
3391	Find $ a_8 $ of a geometric progression if $ a_1 = 9375 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	2
3392	Find $ a_8 $ of a geometric progression if $ a_1 = 9375 ~~ \text{and} ~~ r = 1.25 $.	2
3393	Find $ a_11 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	2
3394	Find $ a_7 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3395	Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
3396	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 4 } = 7 $.	2
3397	Find first element ( $ a_1 $ ) of a geometic progression if $ r = 3 ~~ \text{and} ~~ a_{ 7 } = 4 $.	2
3398	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 4 }{ 729 } ~~ \text{and} ~~ r = 3 $.	2
3399	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 7800 ~~ \text{and} ~~ r = 1.02 $.	2
3400	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 7 } = \frac{ 37 }{ 256 } ~~ \text{and} ~~ a_{ 12 } = 148 $.	2