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
2151	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 4 } \right) $.	3
2152	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 4 $.	3
2153	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	3
2154	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 88 ~~ \text{and} ~~ d = \left( -12 \right) $.	3
2155	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 11 } ~~ \text{and} ~~ d = 0 $.	3
2156	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -2 $.	3
2157	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	3
2158	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	3
2159	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	3
2160	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	3
2161	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = -37 ~~ \text{and} ~~ d = 200 $.	3
2162	Find common difference $ d $ of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ a_{ 112 } = 432 $.	3
2163	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	3
2164	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	3
2165	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	3
2166	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	3
2167	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \left( -21 \right) $.	3
2168	Find $ a_{ 250 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = 5 $.	3
2169	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	3
2170	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2171	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	3
2172	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	3
2173	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	3
2174	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 205 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2175	Find $ a_{ 46 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	3
2176	Find $ a_{ 96 } $ of an arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = \left( -12 \right) $.	3
2177	$$ a_1 = 1 ~,~ d = 2 ~,~ a_n = 4 ~,~ n = ? $$	3
2178	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 5 $.	3
2179	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 9000 $.	3
2180	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 3 $.	3
2181	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2182	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 8 $.	3
2183	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 8 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	3
2184	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \frac{ 8 }{ 5 } $.	3
2185	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = \left( -5 \right) $.	3
2186	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 21 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 6 }{ 5 } \right) $.	3
2187	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	3
2188	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	3
2189	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	3
2190	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 4 $.	3
2191	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	3
2192	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 5 $.	3
2193	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	3
2194	Find $ S_{ 39 } $ ( sum of first $ 39 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	3
2195	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 6 $.	3
2196	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 77 ~~ \text{and} ~~ d = -4 $.	3
2197	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	3
2198	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -38 ~~ \text{and} ~~ d = \left( -100 \right) $.	3
2199	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	3
2200	Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 71 }{ 4 } ~~ \text{and} ~~ a_{ 4 } = \frac{ 113 }{ 4 } $.	3