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
5401	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 4 }{ 5 } $.	2
5402	Find $ S_{ 60000 } $ ( sum of first $ 60000 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
5403	Find $ S_{ 65535 } $ ( sum of first $ 65535 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
5404	Find $ S_{ 65536 } $ ( sum of first $ 65536 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
5405	$$ a_{ 2 } = 15 ~~,~~ S_{ 15 } = 105 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5406	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
5407	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
5408	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 0 $.	2
5409	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5410	$$ a_1 = 18 ~~,~~ d = -2 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5411	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	2
5412	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 1 $.	2
5413	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5414	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5415	$$ a_1 = 15 ~,~ d = 4 ~,~ S_n = 3219 ~,~ n = ? $$	2
5416	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 17200 ~~ \text{and} ~~ d = 1000 $.	2
5417	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 10 $.	2
5418	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 10 $.	2
5419	$$ a_1 = 2 ~,~ d = 5 ~,~ a_n = 302 ~,~ n = ? $$	2
5420	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
5421	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 35 $.	2
5422	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
5423	Find $ d $ (common difference of arithmetic progression) if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ S_{ 2 } = \frac{ 23 }{ 12 } $.	2
5424	Find $ d $ (common difference of arithmetic progression) if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ S_{ 3 } = \frac{ 211 }{ 60 } $.	2
5425	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
5426	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
5427	$$ a_1 = \frac{ 1 }{ 10 } ~~,~~ d = \frac{ 7 }{ 100 } ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5428	Find $ a_1 $ (first term of arithmetic progression) if $ d = \frac{ 7 }{ 100 } ~~ \text{and} ~~ S_{ 50 } = 100 $.	2
5429	Find $ S_{ 88 } $ ( sum of first $ 88 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $.	2
5430	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -200 ~~ \text{and} ~~ d = 200 $.	2
5431	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 9 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	2
5432	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5433	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 10 $.	2
5434	$$ a_1 = 4 ~,~ d = 7 ~,~ a_n = 25 ~,~ n = ? $$	2
5435	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 11 $.	2
5436	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5437	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	2
5438	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 12 $.	2
5439	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = -1 $.	2
5440	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $.	2
5441	Find $ S_{ 334 } $ ( sum of first $ 334 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5442	Find $ S_{ 777 } $ ( sum of first $ 777 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = -3 $.	2
5443	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	2
5444	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 7 }{ 20 } ~~ \text{and} ~~ d = -4 $.	2
5445	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
5446	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
5447	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
5448	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	2
5449	$$ a_1 = 2 ~,~ d = 3 ~,~ a_n = 15 ~,~ n = ? $$	2
5450	$$ a_1 = 231 ~,~ d = 1 ~,~ a_n = 463 ~,~ n = ? $$	2