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
401	$$ a_1 = -2 ~,~ d = -10 ~,~ S_n = -224 ~,~ n = ? $$	7
402	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	7
403	Find $ S_{ 2017 } $ ( sum of first $ 2017 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	7
404	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	7
405	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 4 $.	7
406	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 3 $.	7
407	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -\frac{ 200 }{ 7 } ~~ \text{and} ~~ d = \frac{ 44 }{ 7 } $.	7
408	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 2 $.	7
409	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	7
410	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -9 \right) $.	7
411	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 5 $.	7
412	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = \left( -6 \right) $.	7
413	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	7
414	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 0 $.	7
415	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 146 $.	7
416	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	7
417	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	7
418	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	7
419	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 7 $.	7
420	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -3 $.	7
421	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	7
422	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	7
423	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -3 \right) $.	7
424	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	7
425	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	7
426	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	7
427	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 253 ~~ \text{and} ~~ d = \left( -5 \right) $.	7
428	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	7
429	Find $ a_{ 432 } $ of an arithmetic progression if $ a_1 = 105 ~~ \text{and} ~~ d = 9 $.	7
430	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	7
431	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	7
432	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	7
433	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	7
434	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	7
435	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = -5 $.	7
436	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -4 \right) $.	7
437	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 11 $.	7
438	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	7
439	Find $ S_{ 63 } $ ( sum of first $ 63 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	7
440	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	7
441	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	7
442	Find $ a_{ 96 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -13 \right) $.	7
443	Find $ a_{ 365 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	7
444	Find $ S_{ 76 } $ ( sum of first $ 76 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -3 $.	7
445	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	7
446	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 1 $.	7
447	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	7
448	Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	7
449	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	7
450	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -\frac{ 4 }{ 5 } \right) $.	7