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
2201	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 15 $.	3
2202	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = -\frac{ 5 }{ 2 } $.	3
2203	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 2505 ~~ \text{and} ~~ d = 5 $.	3
2204	Find $ S_{ 82 } $ ( sum of first $ 82 $ terms ) of arithmetic progression if $ a_1 = 350 ~~ \text{and} ~~ d = 35 $.	3
2205	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2206	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	3
2207	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $.	3
2208	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	3
2209	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 4 $.	3
2210	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	3
2211	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 2505 ~~ \text{and} ~~ d = 5 $.	3
2212	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	3
2213	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	3
2214	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	3
2215	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = \frac{ 38 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	3
2216	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 5 $.	3
2217	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = -\frac{ 7 }{ 2 } $.	3
2218	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	3
2219	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 3899 ~~ \text{and} ~~ d = 4 $.	3
2220	$$ a_1 = 1 ~,~ d = 2 ~,~ a_n = 37 ~,~ n = ? $$	3
2221	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 99 ~~ \text{and} ~~ d = -1 $.	3
2222	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	3
2223	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	3
2224	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 4 $.	3
2225	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	3
2226	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	3
2227	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 50876 ~~ \text{and} ~~ d = 1500 $.	3
2228	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	3
2229	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 2 $.	3
2230	Find $ S_{ 121 } $ ( sum of first $ 121 $ terms ) of arithmetic progression if $ a_1 = 68 ~~ \text{and} ~~ d = 99 $.	3
2231	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	3
2232	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 840 ~~ \text{and} ~~ d = -5 $.	3
2233	Find $ S_{ 47 } $ ( sum of first $ 47 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = -9 $.	3
2234	$$ a_1 = -16 ~,~ d = -10 ~,~ S_n = -1818 ~,~ n = ? $$	3
2235	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	3
2236	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 91 ~~ \text{and} ~~ d = 1 $.	3
2237	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	3
2238	Find $ S_{ 250 } $ ( sum of first $ 250 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2239	Find $ S_{ 336 } $ ( sum of first $ 336 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $.	3
2240	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	3
2241	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 0 $.	3
2242	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 4 $.	3
2243	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = \frac{ 19 }{ 5 } $.	3
2244	Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -6 \right) $.	3
2245	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 10 $.	3
2246	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 100 $.	3
2247	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	3
2248	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 10 $.	3
2249	Find $ a_{ 149 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	3
2250	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 729 $.	3