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
3551	Find $ a_4 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 6 $.	2
3552	Find $ a_6 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -4 $.	2
3553	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -0.125 $.	2
3554	Find $ a_1 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	2
3555	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 15 ~~ \text{and} ~~ r = \frac{ 9 }{ 10 } $.	2
3556	Find $ a_1 $ of a geometric progression if $ a_1 = 400 ~~ \text{and} ~~ r = 1.5 $.	2
3557	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 64 ~~ \text{and} ~~ a_{ 4 } = 384 $.	2
3558	Find $ a_5 $ of a geometric progression if $ a_1 = -8 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	2
3559	Find $ a_7 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
3560	Find $ a_10 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 6 $.	2
3561	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 20 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3562	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 150 ~~ \text{and} ~~ r = -\frac{ 5 }{ 3 } $.	2
3563	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	2
3564	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 27 ~~ \text{and} ~~ r = -\frac{ 5 }{ 3 } $.	2
3565	Find $ a_200 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3566	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = \dfrac{ 27 }{ 32 } $.	2
3567	Find $ a_12 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 2 $.	2
3568	Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 2 } = 2 ~~ \text{and} ~~ a_{ 5 } = 8 $.	2
3569	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	2
3570	Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 3 $.	2
3571	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 11 ~~ \text{and} ~~ r = 4 $.	2
3572	Find $ a_5 $ of a geometric progression if $ a_1 = -15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
3573	Find $ a_12 $ of a geometric progression if $ a_1 = -15 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
3574	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = -15 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
3575	Find $ a_6 $ of a geometric progression if $ a_1 = -36 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3576	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1 $.	2
3577	Find $ a_6 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 2 $.	2
3578	Find $ a_25 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	2
3579	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 400000 ~~ \text{and} ~~ r = 1.05 $.	2
3580	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	2
3581	Find $ a_20 $ of a geometric progression if $ a_1 = 0.002739 ~~ \text{and} ~~ r = 0.002739 $.	2
3582	Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = 36000 ~~ \text{and} ~~ r = 1.072 $.	2
3583	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 1.123 $.	2
3584	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 400000 ~~ \text{and} ~~ r = 1.12 $.	2
3585	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -2 $.	2
3586	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 1.028 ~~ \text{and} ~~ r = 1.028 $.	2
3587	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3588	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 6 }{ 5 } ~~ \text{and} ~~ r = 1.005 $.	2
3589	Find $ a_3 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3590	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3591	Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 3 } = 36 $.	2
3592	Find $ a_12 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	2
3593	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 5 } $.	2
3594	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = 2 $.	2
3595	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 8 } ~~ \text{and} ~~ r = -0.125 $.	2
3596	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 4 $.	2
3597	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = -2 $.	2
3598	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	2
3599	Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 7 }{ 6 } ~~ \text{and} ~~ r = \dfrac{ 7 }{ 6 } $.	2
3600	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 45 ~~ \text{and} ~~ r = \frac{ 3 }{ 5 } $.	2