Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

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ID	Problem	Count
451	Find $ S_{ 168 } $ ( sum of first $ 168 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	7
452	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	7
453	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 5 $.	7
454	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 7 $.	7
455	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	7
456	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	7
457	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 8 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	6
458	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -55 ~~ \text{and} ~~ d = 2 $.	6
459	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	6
460	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 6 $.	6
461	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	6
462	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 15 $.	6
463	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	6
464	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	6
465	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	6
466	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	6
467	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	6
468	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 6 $.	6
469	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	6
470	Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 3 $.	6
471	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $.	6
472	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	6
473	Find $ a_{ 92 } $ of an arithmetic progression if $ a_1 = -29 ~~ \text{and} ~~ d = 7 $.	6
474	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	6
475	Find common difference $ d $ of arithmetic progression if $ a_1 = 43 ~~ \text{and} ~~ a_{ 3 } = 35 $.	6
476	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	6
477	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	6
478	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	6
479	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	6
480	Find $ S_{ 51 } $ ( sum of first $ 51 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	6
481	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -3 \right) $.	6
482	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	6
483	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 8 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	6
484	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	6
485	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	6
486	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 4 $.	6
487	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 6 $.	6
488	Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 3 } = \frac{ 1 }{ 3 } $.	6
489	Find $ a_{ 503 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	6
490	Find $ S_{ 304 } $ ( sum of first $ 304 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	6
491	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 46 }{ 5 } ~~ \text{and} ~~ d = \frac{ 21 }{ 10 } $.	6
492	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = -\frac{ 25 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 10 } \right) $.	6
493	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	6
494	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	6
495	$$ a_1 = 10 ~,~ d = 10 ~,~ S_n = 1000000 ~,~ n = ? $$	6
496	$$ a_1 = 3 ~~,~~ d = 5 ~~,~~ a_1 = ? ~~,~~ d = ? $$	6
497	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	6
498	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 260 ~~ \text{and} ~~ d = \left( -5 \right) $.	6
499	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = 89 ~~ \text{and} ~~ d = 79 $.	6
500	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = \left( -8 \right) $.	6