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
401	Find $ a_13 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 2 $.	10
402	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = 2 $.	10
403	Find $ a_12 $ of a geometric progression if $ a_1 = -1 ~~ \text{and} ~~ r = 3 $.	10
404	Find $ a_4 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = 6 $.	10
405	Find $ a_10 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	10
406	Find $ a_7 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -5 $.	10
407	Find $ a_10 $ of a geometric progression if $ a_1 = 72 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	10
408	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	10
409	Find $ a_7 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	10
410	$$ a_1 = 10 ~,~ r = \frac{ 11 }{ 50 } ~,~ S_n = 360 ~,~ n = ? $$	10
411	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 120 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	10
412	Find $ a_5 $ of a geometric progression if $ a_1 = 578 ~~ \text{and} ~~ r = 7 $.	10
413	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 5 $.	10
414	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 10 } $.	10
415	Find $ a_9 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	9
416	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	9
417	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -2 $.	9
418	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	9
419	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 5 $.	9
420	Find $ a_6 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	9
421	Find $ a_7 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.	9
422	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 6 ~~ \text{and} ~~ r = 3 $.	9
423	Find the sum of the first $ 13 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 4 $.	9
424	Find $ a_3 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 5 $.	9
425	Find $ a_12 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = 2 $.	9
426	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 0 ~~ \text{and} ~~ r = 3 $.	9
427	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 4 $.	9
428	Find $ a_14 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -5 $.	9
429	Find $ a_8 $ of a geometric progression if $ a_1 = -2 ~~ \text{and} ~~ r = 5 $.	9
430	Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = 2 $.	9
431	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 512 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	9
432	Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = -20 ~~ \text{and} ~~ r = 2 $.	9
433	Find $ a_10 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	9
434	Find $ a_5 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	9
435	Find $ a_7 $ of a geometric progression if $ a_1 = 6 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 2 } $.	9
436	Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 64 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	9
437	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	9
438	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.	9
439	Find $ a_20 $ of a geometric progression if $ a_1 = 15000 ~~ \text{and} ~~ r = 1.1 $.	9
440	Find $ a_25 $ of a geometric progression if $ a_1 = 20000 ~~ \text{and} ~~ r = 1.1 $.	9
441	Find $ a_25 $ of a geometric progression if $ a_1 = 15000 ~~ \text{and} ~~ r = 1.1 $.	9
442	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -2 $.	9
443	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 5 $.	9
444	Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	9
445	Find $ a_15 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	9
446	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ r = \frac{ 2 }{ 5 } $.	9
447	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.	9
448	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 2 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 4 }{ 3 } $.	9
449	Find $ a_5 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = \dfrac{ 61 }{ 50 } $.	9
450	Find $ a_7 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $.	9