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
5101	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	2
5102	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 70 ~~ \text{and} ~~ d = 1 $.	2
5103	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 98 ~~ \text{and} ~~ d = 1 $.	2
5104	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 98 ~~ \text{and} ~~ d = 1 $.	2
5105	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 1 $.	2
5106	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 69 ~~ \text{and} ~~ d = 1 $.	2
5107	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 4 $.	2
5108	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 4 $.	2
5109	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 0.001 ~~ \text{and} ~~ d = 0.0001 $.	2
5110	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = 0.001 $.	2
5111	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 280 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
5112	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 280 ~~ \text{and} ~~ d = -8 $.	2
5113	$$ a_1 = 46 ~,~ d = \frac{ 71 }{ 500 } ~,~ a_n = 16 ~,~ n = ? $$	2
5114	$$ a_1 = 3 ~,~ d = 2 ~,~ S_n = 47000000 ~,~ n = ? $$	2
5115	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5116	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 5 $.	2
5117	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 62 ~~ \text{and} ~~ d = 5 $.	2
5118	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 7 $.	2
5119	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 4 $.	2
5120	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
5121	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = 0 $.	2
5122	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	2
5123	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	2
5124	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = 5 $.	2
5125	Find $ a_{ 250 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 5 $.	2
5126	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 190 ~~ \text{and} ~~ d = \left( -60 \right) $.	2
5127	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 190 ~~ \text{and} ~~ d = \left( -60 \right) $.	2
5128	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 190 ~~ \text{and} ~~ d = \left( -60 \right) $.	2
5129	Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 5 $.	2
5130	Find $ a_{ 14192429 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 5 $.	2
5131	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $.	2
5132	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 7 $.	2
5133	$$ a_1 = 315 ~,~ d = 11 ~,~ a_n = 18 ~,~ n = ? $$	2
5134	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 6 $.	2
5135	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5136	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 1 $.	2
5137	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = -3 $.	2
5138	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 4 $.	2
5139	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 4 $.	2
5140	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
5141	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 240 ~~ \text{and} ~~ d = 6 $.	2
5142	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 240 ~~ \text{and} ~~ d = 6 $.	2
5143	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $.	2
5144	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 58 ~~ \text{and} ~~ d = 0 $.	2
5145	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 6 $.	2
5146	Find $ a_{ 75 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = 95 $.	2
5147	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 95 ~~ \text{and} ~~ d = 2 $.	2
5148	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 2 $.	2
5149	Find $ a_{ 44 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = 22 $.	2
5150	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 66 ~~ \text{and} ~~ d = 49 $.	2