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
3751	Find $ a_20 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3752	Find $ a_10 $ of a geometric progression if $ a_1 = 8000 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	2
3753	Find $ a_10 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = -2 $.	2
3754	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	2
3755	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 10 ~~ \text{and} ~~ a_{ 3 } = 40 $.	2
3756	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 0.3957 ~~ \text{and} ~~ r = 0.9523 $.	2
3757	Find $ a_7 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3758	Find $ a_9 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3759	Find $ a_12 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3760	Find $ a_11 $ of a geometric progression if $ a_1 = 32 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	2
3761	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 3 } = 7 $.	2
3762	Find $ a_1 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1.871 $.	2
3763	Find $ a_2 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1.871 $.	2
3764	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 625 ~~ \text{and} ~~ a_{ 4 } = 135 $.	2
3765	$$ a_1 = 625 ~,~ r = \frac{ 3 }{ 5 } ~,~ a_n = 6 ~,~ n = ? $$	2
3766	Find first element ( $ a_1 $ ) of a geometic progression if $ r = \frac{ 3 }{ 5 } ~~ \text{and} ~~ a_{ 3 } = 225 $.	2
3767	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 625 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2
3768	Find the sum of the first $ 99999999999 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 32 } ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	2
3769	Find $ a_6 $ of a geometric progression if $ a_1 = 625 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
3770	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 3 } = 27 $.	2
3771	Find $ a_13 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	2
3772	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 810 ~~ \text{and} ~~ a_{ 4 } = 3750 $.	2
3773	Find $ a_4 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $.	2
3774	Find $ a_7 $ of a geometric progression if $ a_1 = 810 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	2
3775	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 324 ~~ \text{and} ~~ r = -6 $.	2
3776	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
3777	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 4 $.	2
3778	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $.	2
3779	Find $ a_7 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -1.667 $.	2
3780	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -4 $.	2
3781	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 4 $.	2
3782	Find $ a_5 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 1 $.	2
3783	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 2 } $.	2
3784	Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3785	Find $ a_9 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = -2 $.	2
3786	Find $ a_18 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	2
3787	Find $ a_4 $ of a geometric progression if $ a_1 = 16 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3788	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 32 } ~~ \text{and} ~~ r = 2 $.	2
3789	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -5 $.	2
3790	Find $ a_24 $ of a geometric progression if $ a_1 = 17 ~~ \text{and} ~~ r = 15 $.	2
3791	Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	2
3792	Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 5 } $.	2
3793	Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = 0.6 $.	2
3794	Find $ a_100 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3795	Find $ a_4 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 0.4 $.	2
3796	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.03 $.	2
3797	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
3798	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3799	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 103 }{ 100 } $.	2
3800	Find the sum of the first $ 200 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 103 }{ 100 } $.	2