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
6851	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 5 $.	1
6852	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -25 \right) $.	1
6853	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = 4 $.	1
6854	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 77 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6855	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 6 $.	1
6856	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = -27 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6857	$$ a_1 = 32 ~,~ d = 7 ~,~ a_n = 1 ~,~ n = ? $$	1
6858	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 61 ~~ \text{and} ~~ d = 8 $.	1
6859	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6860	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	1
6861	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	1
6862	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
6863	Find $ a_{ 110 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	1
6864	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = -7 $.	1
6865	Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 1 $.	1
6866	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
6867	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 4 $.	1
6868	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	1
6869	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $.	1
6870	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
6871	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
6872	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	1
6873	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 133 ~~ \text{and} ~~ d = 5 $.	1
6874	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1
6875	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
6876	Find $ S_{ 899 } $ ( sum of first $ 899 $ terms ) of arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = 1 $.	1
6877	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	1
6878	Find $ S_{ 80 } $ ( sum of first $ 80 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	1
6879	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	1
6880	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 7 $.	1
6881	Find $ a_1 $ (first term of arithmetic progression) if $ d = -7 ~~ \text{and} ~~ a_{ 3 } = 72 $.	1
6882	Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 29 }{ 4 } ~~ \text{and} ~~ a_{ 4 } = \frac{ 47 }{ 4 } $.	1
6883	$$ a_1 = \frac{ 29 }{ 4 } ~,~ d = \frac{ 3 }{ 2 } ~,~ a_n = 30 ~,~ n = ? $$	1
6884	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 29 }{ 4 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	1
6885	Find common difference $ d $ of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ a_{ 4 } = 22 $.	1
6886	Find common difference $ d $ of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ a_{ 20 } = 136 $.	1
6887	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
6888	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
6889	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
6890	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $.	1
6891	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	1
6892	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
6893	Find $ S_{ 224 } $ ( sum of first $ 224 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 4 }{ 5 } $.	1
6894	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 2 $.	1
6895	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 2 $.	1
6896	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 5 $.	1
6897	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 12 $.	1
6898	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 17 $.	1
6899	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 16 $.	1
6900	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = -\frac{ 3 }{ 2 } $.	1