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
3601	Find $ a_11 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	2
3602	Find $ a_15 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 4 $.	2
3603	Find $ a_9 $ of a geometric progression if $ a_1 = 75 ~~ \text{and} ~~ r = 1.042 $.	2
3604	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -3 $.	2
3605	Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 5 } $.	2
3606	Find the sum of the first $ 31 $ terms of a geometric sequence if $ a_1 = 365 ~~ \text{and} ~~ r = -1 $.	2
3607	Find $ a_4 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 8 } $.	2
3608	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 36 ~~ \text{and} ~~ r = -3 $.	2
3609	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
3610	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
3611	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -6 $.	2
3612	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -6 $.	2
3613	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -\frac{ 2 }{ 3 } $.	2
3614	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 17 ~~ \text{and} ~~ r = 2 $.	2
3615	Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ r = \frac{ 1 }{ 5 } $.	2
3616	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 50 ~~ \text{and} ~~ r = 0.9174 $.	2
3617	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 0.9174 $.	2
3618	Find $ a_10 $ of a geometric progression if $ a_1 = 40 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
3619	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 7 } ~~ \text{and} ~~ r = \dfrac{ 9 }{ 7 } $.	2
3620	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 23436 ~~ \text{and} ~~ r = 4 $.	2
3621	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3622	Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 4 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	2
3623	Find $ a_4 $ of a geometric progression if $ a_1 = -\dfrac{ 4 }{ 25 } ~~ \text{and} ~~ r = 5 $.	2
3624	Find $ a_20 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = 1.05 $.	2
3625	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 32 $.	2
3626	Find $ a_5 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 20 } $.	2
3627	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 21 }{ 20 } $.	2
3628	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	2
3629	Find the sum of the first $ 24 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.	2
3630	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 89 ~~ \text{and} ~~ r = \frac{ 89 }{ 100 } $.	2
3631	Find $ a_3 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	2
3632	Find $ a_6 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = -3 $.	2
3633	Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 2 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	2
3634	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -6 $.	2
3635	Find $ a_5 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 8 $.	2
3636	Find $ a_5 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = -8 $.	2
3637	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 308 ~~ \text{and} ~~ r = -4 $.	2
3638	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 308 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	2
3639	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = 0.9 $.	2
3640	Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 100 } ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
3641	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = 0.025 $.	2
3642	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = 2.5 $.	2
3643	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 2 $.	2
3644	Find $ a_7 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 3 $.	2
3645	Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 9 $.	2
3646	Find $ a_5 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
3647	Find $ a_9 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	2
3648	Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	2
3649	Find $ a_32 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	2
3650	Find $ a_4 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	2