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
2351	Find $ S_{ 350 } $ ( sum of first $ 350 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	3
2352	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 46 ~~ \text{and} ~~ d = \left( -8 \right) $.	3
2353	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	3
2354	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 9 $.	3
2355	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = \left( -10 \right) $.	3
2356	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 7 $.	3
2357	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 0 $.	3
2358	$$ a_{ 3 } = 3 ~~,~~ S_{ 6 } = 24 ~~,~~ a_1 = ? ~~,~~ d = ? $$	3
2359	Find $ S_{ 1001 } $ ( sum of first $ 1001 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	3
2360	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	3
2361	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	3
2362	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	3
2363	Find $ S_{ 80 } $ ( sum of first $ 80 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	3
2364	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	3
2365	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2366	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = -4 $.	3
2367	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 152 ~~ \text{and} ~~ d = -3 $.	3
2368	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -3 $.	3
2369	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	3
2370	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 10 $.	3
2371	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 11 $.	3
2372	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 11 $.	3
2373	Find $ a_{ 75 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	3
2374	Find $ a_{ 125 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	3
2375	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	3
2376	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	3
2377	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = \left( -7 \right) $.	3
2378	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	3
2379	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 2 $.	3
2380	Find $ a_{ 75 } $ of an arithmetic progression if $ a_1 = -1113 ~~ \text{and} ~~ d = 19 $.	3
2381	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	3
2382	$$ a_1 = 2 ~,~ d = 3 ~,~ a_n = 80 ~,~ n = ? $$	3
2383	Find $ S_{ 96 } $ ( sum of first $ 96 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 10 $.	3
2384	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	3
2385	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -2 \right) $.	3
2386	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = -27 ~~ \text{and} ~~ d = 16 $.	3
2387	Find $ a_{ 82 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 17 $.	3
2388	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 3 $.	3
2389	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -9 \right) $.	3
2390	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $.	3
2391	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	3
2392	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 5 }{ 8 } $.	3
2393	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	3
2394	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 3 $.	3
2395	$$ a_1 = 10 ~,~ d = 10 ~,~ S_n = 45000 ~,~ n = ? $$	3
2396	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 6 $.	3
2397	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 658 $.	3
2398	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	3
2399	Find $ S_{ 255 } $ ( sum of first $ 255 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	3
2400	Find $ S_{ 255 } $ ( sum of first $ 255 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	3