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
351	Find $ a_15 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.1 $.	10
352	Find $ a_15 $ of a geometric progression if $ a_1 = 30000 ~~ \text{and} ~~ r = 1.1 $.	10
353	Find $ a_6 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 10 } ~~ \text{and} ~~ r = 9 $.	10
354	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	10
355	Find $ a_8 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 4 $.	10
356	Find $ a_10 $ of a geometric progression if $ a_1 = -9 ~~ \text{and} ~~ r = -3 $.	10
357	Find $ a_10 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	10
358	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 2 $.	10
359	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	10
360	Find $ a_10 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $.	10
361	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	10
362	Find $ a_5 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $.	10
363	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	10
364	Find $ a_6 $ of a geometric progression if $ a_1 = 800 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	10
365	Find $ a_15 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	10
366	Find $ a_10 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -4 $.	10
367	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 5 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $.	10
368	Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ r = 2 $.	10
369	Find $ a_8 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	10
370	Find $ a_9 $ of a geometric progression if $ a_1 = 9 ~~ \text{and} ~~ r = -2 $.	10
371	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 5 $.	10
372	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -2 $.	10
373	Find $ a_9 $ of a geometric progression if $ a_1 = -65536 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.	10
374	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	10
375	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 10 ~~ \text{and} ~~ r = 1.22 $.	10
376	Find $ a_7 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.	10
377	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.	10
378	Find $ a_4 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 6 $.	10
379	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	10
380	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = \frac{ 1 }{ 100 } $.	10
381	Find $ a_8 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	10
382	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 512 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	10
383	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ r = -2 $.	10
384	Find $ a_10 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	10
385	Find $ a_11 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	10
386	Find $ a_8 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -5 $.	10
387	Find $ a_10 $ of a geometric progression if $ a_1 = 81 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	10
388	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 30 ~~ \text{and} ~~ r = -\frac{ 1 }{ 5 } $.	10
389	Find $ a_12 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = -5 $.	10
390	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $.	10
391	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -8 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.	10
392	Find the sum of the first $ 17 $ terms of a geometric sequence if $ a_1 = 486 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	10
393	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	10
394	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	10
395	Find $ a_12 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = -2 $.	10
396	Find $ a_11 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = -4 $.	10
397	Find $ a_7 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 9 } ~~ \text{and} ~~ r = 3 $.	10
398	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	10
399	Find $ a_3 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 3 $.	10
400	Find $ a_13 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	10