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
6801	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
6802	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 3 $.	1
6803	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
6804	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -37 ~~ \text{and} ~~ d = 2 $.	1
6805	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 20 $.	1
6806	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
6807	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 6 $.	1
6808	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	1
6809	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 7 $.	1
6810	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -84 ~~ \text{and} ~~ d = 11 $.	1
6811	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6812	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 5 $.	1
6813	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 21 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 6 }{ 5 } \right) $.	1
6814	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
6815	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
6816	$$ a_1 = \frac{ 13 }{ 4 } ~,~ d = \frac{ 1 }{ 3 } ~,~ a_n = \frac{ 41 }{ 4 } ~,~ n = ? $$	1
6817	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	1
6818	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6819	Find $ a_{ 199 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	1
6820	$$ a_1 = 0 ~,~ d = 4 ~,~ S_n = 78804 ~,~ n = ? $$	1
6821	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 1 $.	1
6822	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 400 $.	1
6823	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	1
6824	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	1
6825	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	1
6826	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	1
6827	Find $ S_{ 58 } $ ( sum of first $ 58 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	1
6828	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 74 ~~ \text{and} ~~ d = \left( -11 \right) $.	1
6829	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 4 $.	1
6830	Find $ a_1 $ (first term of arithmetic progression) if $ d = -1 ~~ \text{and} ~~ a_{ 8 } = 14 $.	1
6831	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 10 $.	1
6832	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 10 $.	1
6833	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 10 $.	1
6834	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
6835	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	1
6836	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 8 } \right) $.	1
6837	Find $ S_{ 282 } $ ( sum of first $ 282 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
6838	Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $.	1
6839	Find $ S_{ 47 } $ ( sum of first $ 47 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $.	1
6840	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 20 $.	1
6841	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 250000 ~~ \text{and} ~~ d = 12000 $.	1
6842	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = -4 $.	1
6843	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = 3 $.	1
6844	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 8 $.	1
6845	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
6846	Find $ S_{ 32850 } $ ( sum of first $ 32850 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
6847	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
6848	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	1
6849	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 3 $.	1
6850	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 3 $.	1