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
3251	Find $ a_21 $ of a geometric progression if $ a_1 = 25000 ~~ \text{and} ~~ r = 1.1 $.	3
3252	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	3
3253	Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 1.215 $.	3
3254	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -11 ~~ \text{and} ~~ r = -4 $.	3
3255	Find $ a_5 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = 90 $.	3
3256	Find $ a_3 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 9 }{ 10 } $.	3
3257	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 5 $.	3
3258	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	3
3259	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1700000 ~~ \text{and} ~~ r = \frac{ 51 }{ 50 } $.	3
3260	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 8 $.	3
3261	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	3
3262	Find $ a_6 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	3
3263	Find $ a_6 $ of a geometric progression if $ a_1 = -375 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	3
3264	Find $ a_7 $ of a geometric progression if $ a_1 = -375 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $.	3
3265	Find $ a_7 $ of a geometric progression if $ a_1 = -20 ~~ \text{and} ~~ r = -2 $.	3
3266	Find $ a_6 $ of a geometric progression if $ a_1 = 392 ~~ \text{and} ~~ r = 1.627 $.	3
3267	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = 2 $.	3
3268	Find $ a_10 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	3
3269	Find $ a_30 $ of a geometric progression if $ a_1 = 50876 ~~ \text{and} ~~ r = 1.024 $.	3
3270	Find the sum of the first $ 30 $ terms of a geometric sequence if $ a_1 = 50876 ~~ \text{and} ~~ r = 1.024 $.	3
3271	Find $ a_6 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = 0.5 $.	3
3272	Find the sum of the first $ 3 $ terms of a geometric sequence if $ a_1 = 90 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	3
3273	$$ a_1 = 1 ~~,~~ r = 4 ~~,~~ a_1 = ? ~~,~~ r = ? $$	3
3274	Find $ a_15 $ of a geometric progression if $ a_1 = 2187 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	3
3275	Find $ a_5 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = \dfrac{ 7 }{ 2 } $.	3
3276	Find $ a_7 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	3
3277	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	2
3278	Find $ a_11 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 5 $.	2
3279	Find $ a_1000 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	2
3280	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 2 } ~~ \text{and} ~~ r = 2 $.	2
3281	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 6 }{ 5 } $.	2
3282	Find $ a_10 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 10 $.	2
3283	Find $ a_3 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 5 $.	2
3284	Find $ a_9 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	2
3285	Find $ a_9 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = -5 $.	2
3286	Find $ a_1 $ of a geometric progression if $ a_1 = 4800 ~~ \text{and} ~~ r = 1.063 $.	2
3287	Find $ a_10 $ of a geometric progression if $ a_1 = 4800 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	2
3288	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 896 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	2
3289	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 2 }{ 9 } ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	2
3290	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 9700 ~~ \text{and} ~~ r = 1.4 $.	2
3291	Find $ a_13 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	2
3292	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3293	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 9 ~~ \text{and} ~~ r = \frac{ 3 }{ 2 } $.	2
3294	Find $ a_3 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 4 $.	2
3295	Find $ a_3 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 4 $.	2
3296	$$ a_1 = 4 ~,~ r = \frac{ 4 }{ 5 } ~,~ S_n = 19.97 ~,~ n = ? $$	2
3297	$$ a_1 = 8 ~,~ r = 3 ~,~ a_n = 17496 ~,~ n = ? $$	2
3298	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 40 } ~~ \text{and} ~~ r = -4 $.	2
3299	Find $ a_4 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 40 } ~~ \text{and} ~~ r = -4 $.	2
3300	Find $ a_41 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = 6 $.	2