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
6501	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
6502	$$ a_{ 3 } = 22 ~~,~~ S_{ 15 } = 855 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
6503	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
6504	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
6505	Find $ a_1 $ (first term of arithmetic progression) if $ d = 7 ~~ \text{and} ~~ a_{ 2 } = 3 $.	1
6506	Find $ S_{ 10100 } $ ( sum of first $ 10100 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	1
6507	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	1
6508	$$ a_1 = 6 ~,~ d = 8 ~,~ S_n = 10100 ~,~ n = ? $$	1
6509	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 700 ~~ \text{and} ~~ d = \frac{ 3 }{ 25 } $.	1
6510	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 20 $.	1
6511	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = \left( -200 \right) $.	1
6512	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 3 $.	1
6513	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 100 $.	1
6514	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -1 $.	1
6515	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -1 $.	1
6516	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = -1 $.	1
6517	Find $ a_{ 124 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $.	1
6518	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6519	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6520	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6521	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6522	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -2 $.	1
6523	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 152 ~~ \text{and} ~~ d = 3 $.	1
6524	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 15 }{ 4 } $.	1
6525	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
6526	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
6527	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
6528	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6529	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 5 $.	1
6530	Find $ a_{ 328 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 4 $.	1
6531	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 1 $.	1
6532	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
6533	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 40000 ~~ \text{and} ~~ d = 800 $.	1
6534	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
6535	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 40000 ~~ \text{and} ~~ d = 800 $.	1
6536	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	1
6537	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	1
6538	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	1
6539	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6540	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	1
6541	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	1
6542	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	1
6543	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	1
6544	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 12 $.	1
6545	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = 0 $.	1
6546	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
6547	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	1
6548	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	1
6549	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
6550	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	1