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
4801	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = -7 $.	2
4802	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 29 }{ 4 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
4803	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 11 $.	2
4804	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 2500 ~~ \text{and} ~~ d = 500 $.	2
4805	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4806	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 0 $.	2
4807	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 0 $.	2
4808	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
4809	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 3 $.	2
4810	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 34 $.	2
4811	$$ a_1 = 14 ~,~ d = -4 ~,~ S_n = 30 ~,~ n = ? $$	2
4812	$$ a_1 = 14 ~,~ d = -4 ~,~ a_n = -86 ~,~ n = ? $$	2
4813	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 13 $.	2
4814	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 8 $.	2
4815	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 0.195 ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
4816	Find $ S_{ 51 } $ ( sum of first $ 51 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $.	2
4817	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $.	2
4818	Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
4819	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4820	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4821	Find $ a_{ 77 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	2
4822	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
4823	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 6 $.	2
4824	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
4825	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
4826	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 2 $.	2
4827	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 25000 ~~ \text{and} ~~ d = 1500 $.	2
4828	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 47000 ~~ \text{and} ~~ d = 1000 $.	2
4829	$$ a_1 = 38 ~,~ d = 10 ~,~ S_n = 968 ~,~ n = ? $$	2
4830	$$ a_1 = 18 ~,~ d = 9 ~,~ S_n = 585 ~,~ n = ? $$	2
4831	$$ a_1 = 6 ~,~ d = 3 ~,~ S_n = 105 ~,~ n = ? $$	2
4832	Find $ a_{ 209 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	2
4833	Find $ S_{ 102 } $ ( sum of first $ 102 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	2
4834	Find $ a_{ 102 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	2
4835	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -5 $.	2
4836	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 33000 ~~ \text{and} ~~ d = 320 $.	2
4837	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 33000 ~~ \text{and} ~~ d = 320 $.	2
4838	$$ a_{ 64 } = -456 ~~,~~ S_{ 81 } = -575 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4839	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 0 $.	2
4840	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -33 ~~ \text{and} ~~ d = -9 $.	2
4841	Find $ S_{ 660 } $ ( sum of first $ 660 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
4842	Find $ a_{ 888 } $ of an arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 2 $.	2
4843	Find $ S_{ 888 } $ ( sum of first $ 888 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 2 $.	2
4844	Find $ a_{ 224 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	2
4845	Find $ S_{ 224 } $ ( sum of first $ 224 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	2
4846	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = -5 $.	2
4847	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 53 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
4848	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 10 $.	2
4849	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 62 ~~ \text{and} ~~ d = 3 $.	2
4850	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 4 $.	2