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
9451	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 65 ~~ \text{and} ~~ d = 1 $.	1
9452	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
9453	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1510 ~~ \text{and} ~~ d = 300 $.	1
9454	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 1510 ~~ \text{and} ~~ d = 300 $.	1
9455	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 1510 ~~ \text{and} ~~ d = 300 $.	1
9456	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 6010 ~~ \text{and} ~~ d = 300 $.	1
9457	Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = 6010 ~~ \text{and} ~~ d = 300 $.	1
9458	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 6010 ~~ \text{and} ~~ d = 300 $.	1
9459	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 6010 ~~ \text{and} ~~ d = 300 $.	1
9460	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = 6010 ~~ \text{and} ~~ d = 300 $.	1
9461	Find $ S_{ 150 } $ ( sum of first $ 150 $ terms ) of arithmetic progression if $ a_1 = 6010 ~~ \text{and} ~~ d = 300 $.	1
9462	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
9463	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 6010 ~~ \text{and} ~~ d = 300 $.	1
9464	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = 2 $.	1
9465	Find $ S_{ 5000 } $ ( sum of first $ 5000 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	1
9466	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 10 $.	1
9467	$$ a_1 = 4 ~,~ d = 10 ~,~ S_n = 104 ~,~ n = ? $$	1
9468	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -\frac{ 58 }{ 5 } ~~ \text{and} ~~ d = \frac{ 14 }{ 5 } $.	1
9469	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = \frac{ 58 }{ 5 } ~~ \text{and} ~~ d = \frac{ 14 }{ 5 } $.	1
9470	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $.	1
9471	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	1
9472	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 52 $.	1
9473	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 208 }{ 25 } ~~ \text{and} ~~ d = \frac{ 29 }{ 25 } $.	1
9474	Find $ a_{ 62 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 7 $.	1
9475	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 9 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	1
9476	Find $ a_1 $ (first term of arithmetic progression) if $ d = 7 ~~ \text{and} ~~ S_{ 38 } = 8308 $.	1
9477	Find $ S_{ 1137 } $ ( sum of first $ 1137 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
9478	Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = \frac{ 62 }{ 5 } ~~ \text{and} ~~ d = \frac{ 22 }{ 5 } $.	1
9479	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
9480	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 132 ~~ \text{and} ~~ d = 50 $.	1
9481	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 132 ~~ \text{and} ~~ d = 50 $.	1
9482	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 5 $.	1
9483	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 19 $.	1
9484	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 26 $.	1
9485	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 19 $.	1
9486	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 19 $.	1
9487	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 26 $.	1
9488	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 26 $.	1
9489	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 26 $.	1
9490	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
9491	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	1
9492	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	1
9493	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -20 \right) $.	1
9494	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
9495	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -5 $.	1
9496	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -5 $.	1
9497	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 4 $.	1
9498	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	1
9499	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -4 $.	1
9500	$$ a_1 = 3 ~~,~~ d = 4 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1