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
5851	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5852	$$ a_1 = 4 ~,~ d = 6 ~,~ a_n = 2 ~,~ n = ? $$	2
5853	Find $ a_{ 124 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 7 $.	2
5854	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
5855	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
5856	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
5857	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 8 $.	2
5858	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = \frac{ 57 }{ 2 } ~~ \text{and} ~~ d = \frac{ 9 }{ 2 } $.	2
5859	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 16000 ~~ \text{and} ~~ d = 30000 $.	2
5860	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
5861	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
5862	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 7 $.	2
5863	Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $.	2
5864	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $.	2
5865	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
5866	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
5867	$$ a_1 = -5 ~,~ a_n = 45 ~,~ S_n = 120 ~,~ n = ? $$	2
5868	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 0 $.	2
5869	$$ a_1 = 4 ~,~ d = 6 ~,~ a_n = 1354 ~,~ n = ? $$	2
5870	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 4 $.	2
5871	Find $ S_{ 170 } $ ( sum of first $ 170 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5872	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 0 $.	2
5873	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 14 $.	2
5874	Find common difference $ d $ of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ a_{ 26 } = 165 $.	2
5875	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 7 $.	2
5876	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	2
5877	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 7 $.	2
5878	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	2
5879	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 46850 ~~ \text{and} ~~ d = 0 $.	2
5880	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 35 $.	2
5881	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
5882	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
5883	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = 14 $.	2
5884	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
5885	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -8 $.	2
5886	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
5887	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
5888	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 9 }{ 2 } ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $.	2
5889	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 620 ~~ \text{and} ~~ d = 463 $.	2
5890	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 620 ~~ \text{and} ~~ d = 132 $.	2
5891	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 10 $.	2
5892	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 2 $.	2
5893	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = 10 $.	2
5894	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5895	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = -3 $.	2
5896	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 3 $.	2
5897	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 37 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 2 }{ 5 } \right) $.	2
5898	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = \frac{ 49 }{ 10 } ~~ \text{and} ~~ d = \frac{ 49 }{ 5 } $.	2
5899	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = \left( -420 \right) $.	2
5900	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2