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
5351	Find $ S_{ 81 } $ ( sum of first $ 81 $ terms ) of arithmetic progression if $ a_1 = 71 ~~ \text{and} ~~ d = 14 $.	2
5352	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 93 }{ 10 } $.	2
5353	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	2
5354	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 7 $.	2
5355	Find common difference $ d $ of arithmetic progression if $ a_1 = -\frac{ 7 }{ 2 } ~~ \text{and} ~~ a_{ 9 } = \frac{ 25 }{ 2 } $.	2
5356	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ d = \frac{ 1 }{ 12 } $.	2
5357	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ d = \frac{ 1 }{ 12 } $.	2
5358	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
5359	Find $ S_{ 270 } $ ( sum of first $ 270 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
5360	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	2
5361	Find $ a_{ 365 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
5362	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5363	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 20 } ~~ \text{and} ~~ d = \frac{ 7 }{ 20 } $.	2
5364	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 7 }{ 20 } $.	2
5365	Find $ S_{ 112 } $ ( sum of first $ 112 $ terms ) of arithmetic progression if $ a_1 = 555 ~~ \text{and} ~~ d = 4 $.	2
5366	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
5367	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 4 $.	2
5368	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 20 $.	2
5369	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 3 $.	2
5370	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 60000 ~~ \text{and} ~~ d = 6000 $.	2
5371	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $.	2
5372	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 32 $.	2
5373	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $.	2
5374	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $.	2
5375	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 1 $.	2
5376	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $.	2
5377	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $.	2
5378	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 2400 ~~ \text{and} ~~ d = 0 $.	2
5379	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 2400 ~~ \text{and} ~~ d = 1.011 $.	2
5380	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 6 } ~~ \text{and} ~~ d = 4 $.	2
5381	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5382	Find $ S_{ 360 } $ ( sum of first $ 360 $ terms ) of arithmetic progression if $ a_1 = 331 ~~ \text{and} ~~ d = 1 $.	2
5383	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
5384	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5385	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
5386	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	2
5387	$$ a_1 = \frac{ 4 }{ 5 } ~,~ a_n = 4 ~,~ S_n = \frac{ 143 }{ 25 } ~,~ n = ? $$	2
5388	$$ a_1 = 15 ~,~ d = 3 ~,~ a_n = 312 ~,~ n = ? $$	2
5389	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	2
5390	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 6 $.	2
5391	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 4 $.	2
5392	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 11 $.	2
5393	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 6 $.	2
5394	$$ a_1 = 6 ~~,~~ d = 12 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5395	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	2
5396	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $.	2
5397	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 215 }{ 2 } ~~ \text{and} ~~ d = \frac{ 75 }{ 2 } $.	2
5398	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	2
5399	Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 5000 $.	2
5400	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $.	2