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
9301	Find $ a_8 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = 6 $.	1
9302	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 16 } ~~ \text{and} ~~ r = -2 $.	1
9303	Find $ a_40 $ of a geometric progression if $ a_1 = 2352 ~~ \text{and} ~~ r = 1.07 $.	1
9304	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -\frac{ 2 }{ 7 } ~~ \text{and} ~~ r = -\frac{ 2 }{ 7 } $.	1
9305	Find the sum of the first $ 18 $ terms of a geometric sequence if $ a_1 = 16 ~~ \text{and} ~~ r = 2 $.	1
9306	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 10 $.	1
9307	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 40 ~~ \text{and} ~~ r = -28 $.	1
9308	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = -\frac{ 2 }{ 5 } $.	1
9309	Find $ a_11 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $.	1
9310	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	1
9311	Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.	1
9312	Find $ a_8 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 4 $.	1
9313	Find $ a_10 $ of a geometric progression if $ a_1 = -65536 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	1
9314	Find $ a_10 $ of a geometric progression if $ a_1 = -65536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 4 } $.	1
9315	Find $ a_9 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9316	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 96 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9317	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 0.125 ~~ \text{and} ~~ r = -2 $.	1
9318	Find $ a_6 $ of a geometric progression if $ a_1 = 0.125 ~~ \text{and} ~~ r = -2 $.	1
9319	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 256 ~~ \text{and} ~~ r = \frac{ 1 }{ 4 } $.	1
9320	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 32 ~~ \text{and} ~~ r = \frac{ 5 }{ 2 } $.	1
9321	Find the sum of the first $ 63 $ terms of a geometric sequence if $ a_1 = 1.004 ~~ \text{and} ~~ r = 1 $.	1
9322	Find $ a_5 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 4 }{ 5 } $.	1
9323	Find $ a_3 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 11 } $.	1
9324	Find $ a_5 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	1
9325	Find $ a_5 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $.	1
9326	Find $ a_2 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = -3 $.	1
9327	Find $ a_3 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9328	Find $ a_4 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9329	Find $ a_5 $ of a geometric progression if $ a_1 = 347 ~~ \text{and} ~~ r = \dfrac{ 5 }{ 4 } $.	1
9330	Find $ a_5 $ of a geometric progression if $ a_1 = 240 ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 4 } $.	1
9331	Find $ a_7 $ of a geometric progression if $ a_1 = 96 ~~ \text{and} ~~ r = 2 $.	1
9332	Find $ a_6 $ of a geometric progression if $ a_1 = -54 ~~ \text{and} ~~ r = -3 $.	1
9333	Find $ a_4 $ of a geometric progression if $ a_1 = 1055026 ~~ \text{and} ~~ r = 1.02 $.	1
9334	Find $ a_6 $ of a geometric progression if $ a_1 = 720 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9335	Find $ a_10 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -2 $.	1
9336	Find $ a_10 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	1
9337	Find $ a_4 $ of a geometric progression if $ a_1 = 3555 ~~ \text{and} ~~ r = \dfrac{ 26 }{ 25 } $.	1
9338	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -2 ~~ \text{and} ~~ r = -4 $.	1
9339	Find $ a_9 $ of a geometric progression if $ a_1 = -125 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	1
9340	Find $ a_9 $ of a geometric progression if $ a_1 = -125 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 5 } $.	1
9341	$$ a_1 = 60 ~,~ r = 0.9 ~,~ S_n = 462.7 ~,~ n = ? $$	1
9342	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 3000000 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9343	Find the sum of the first $ 1 $ terms of a geometric sequence if $ a_1 = 3000000 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9344	Find the sum of the first $ 2 $ terms of a geometric sequence if $ a_1 = 3000000 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	1
9345	Find $ a_2 $ of a geometric progression if $ a_1 = 3000000 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	1
9346	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9347	Find $ a_5 $ of a geometric progression if $ a_1 = 650000 ~~ \text{and} ~~ r = 0.035 $.	1
9348	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	1
9349	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $.	1
9350	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 0.00075 ~~ \text{and} ~~ r = \frac{ 13 }{ 10 } $.	1