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
5901	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	2
5902	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
5903	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
5904	$$ a_1 = -17 ~,~ d = -6 ~,~ a_n = 37 ~,~ n = ? $$	2
5905	$$ a_1 = 18 ~,~ d = -8 ~,~ a_n = 24 ~,~ n = ? $$	2
5906	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 2 $.	2
5907	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	2
5908	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 2 $.	2
5909	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	2
5910	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	2
5911	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
5912	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
5913	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 1 $.	2
5914	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \frac{ 12 }{ 5 } $.	2
5915	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \frac{ 12 }{ 5 } $.	2
5916	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	2
5917	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 0 $.	2
5918	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 74 $.	2
5919	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5920	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 20 $.	2
5921	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 3 $.	2
5922	Find $ a_1 $ (first term of arithmetic progression) if $ d = 8 ~~ \text{and} ~~ S_{ 35 } = 5005 $.	2
5923	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	2
5924	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	2
5925	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 50 $.	2
5926	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 13 $.	2
5927	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 8 $.	2
5928	$$ a_{ 7 } = 34 ~~,~~ S_{ 20 } = 1170 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5929	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = -4 $.	2
5930	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	2
5931	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -1 $.	2
5932	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	2
5933	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	2
5934	Find $ S_{ 182 } $ ( sum of first $ 182 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5935	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 12 $.	2
5936	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 4 }{ 3 } ~~ \text{and} ~~ d = \frac{ 11 }{ 7 } $.	2
5937	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 1 $.	2
5938	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 1 $.	2
5939	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 1 $.	2
5940	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
5941	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $.	2
5942	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $.	2
5943	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	2
5944	Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $.	2
5945	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 50 $.	2
5946	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 7 $.	2
5947	Find $ S_{ 145 } $ ( sum of first $ 145 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
5948	$$ a_1 = -12 ~,~ d = 3 ~,~ a_n = 1104 ~,~ n = ? $$	2
5949	Find $ S_{ 71 } $ ( sum of first $ 71 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 3 $.	2
5950	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 1800 ~~ \text{and} ~~ d = 100 $.	2