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
2101	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	3
2102	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	3
2103	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 3 } \right) $.	3
2104	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	3
2105	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 0 $.	3
2106	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -5 \right) $.	3
2107	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = 19 $.	3
2108	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 12 } ~~ \text{and} ~~ d = \frac{ 1 }{ 12 } $.	3
2109	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	3
2110	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 150 $.	3
2111	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 4 $.	3
2112	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 28000 ~~ \text{and} ~~ d = 800 $.	3
2113	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = \left( -\frac{ 5 }{ 2 } \right) $.	3
2114	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 5 $.	3
2115	$$ a_{ 26 } = 113 ~~,~~ S_{ 35 } = 2275 ~~,~~ a_1 = ? ~~,~~ d = ? $$	3
2116	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \left( -6 \right) $.	3
2117	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2118	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -1 $.	3
2119	Find $ S_{ 51 } $ ( sum of first $ 51 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	3
2120	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 16 $.	3
2121	Find $ S_{ 900 } $ ( sum of first $ 900 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	3
2122	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	3
2123	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 8 $.	3
2124	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2125	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	3
2126	Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 4 $.	3
2127	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 7 $.	3
2128	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2129	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	3
2130	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $.	3
2131	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 9 $.	3
2132	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	3
2133	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	3
2134	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	3
2135	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	3
2136	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	3
2137	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = \frac{ 7 }{ 10 } $.	3
2138	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -20 \right) $.	3
2139	Find $ a_{ 118 } $ of an arithmetic progression if $ a_1 = \frac{ 131 }{ 25 } ~~ \text{and} ~~ d = \frac{ 11 }{ 20 } $.	3
2140	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2141	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \left( -9 \right) $.	3
2142	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 51 }{ 10 } $.	3
2143	Find $ a_{ 212 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	3
2144	$$ a_1 = -95 ~,~ d = -10 ~,~ a_n = 38 ~,~ n = ? $$	3
2145	Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2146	Find $ S_{ 9400 } $ ( sum of first $ 9400 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2147	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 30 $.	3
2148	$$ a_1 = 5 ~,~ d = -1 ~,~ a_n = -9 ~,~ n = ? $$	3
2149	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 8 $.	3
2150	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = \frac{ 87 }{ 10 } ~~ \text{and} ~~ d = -\frac{ 31 }{ 10 } $.	3