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
6601	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
6602	$$ d = 2 ~,~ a_n = 4 ~,~ S_n = -14 ~,~ n = ? $$	1
6603	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = -3 $.	1
6604	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 4 $.	1
6605	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 5 $.	1
6606	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 8 $.	1
6607	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 52 ~~ \text{and} ~~ d = 3 $.	1
6608	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
6609	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	1
6610	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 20000 ~~ \text{and} ~~ d = 20000 $.	1
6611	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 20000 ~~ \text{and} ~~ d = 200 $.	1
6612	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 4 $.	1
6613	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 4 $.	1
6614	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = \frac{ 13 }{ 6 } ~~ \text{and} ~~ d = \left( -\frac{ 6 }{ 5 } \right) $.	1
6615	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.	1
6616	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.	1
6617	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 1050 ~~ \text{and} ~~ d = 150 $.	1
6618	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -20 \right) $.	1
6619	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = -20 $.	1
6620	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -13 \right) $.	1
6621	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -\frac{ 94 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 13 }{ 3 } \right) $.	1
6622	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
6623	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 13 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	1
6624	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 7 $.	1
6625	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 4 $.	1
6626	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 6 $.	1
6627	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 6 $.	1
6628	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
6629	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	1
6630	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
6631	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
6632	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = -2 $.	1
6633	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6634	Find $ a_{ 2000 } $ of an arithmetic progression if $ a_1 = 298375 ~~ \text{and} ~~ d = \left( -1703 \right) $.	1
6635	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 396 ~~ \text{and} ~~ d = \frac{ 198 }{ 25 } $.	1
6636	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 396 ~~ \text{and} ~~ d = \frac{ 198 }{ 25 } $.	1
6637	$$ a_1 = 10 ~,~ d = 2 ~,~ S_n = 450 ~,~ n = ? $$	1
6638	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 0 $.	1
6639	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 98 $.	1
6640	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 7 $.	1
6641	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 4 $.	1
6642	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 89 ~~ \text{and} ~~ d = -3 $.	1
6643	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = 4 $.	1
6644	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $.	1
6645	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $.	1
6646	Find $ S_{ 37 } $ ( sum of first $ 37 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 8 $.	1
6647	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 365 ~~ \text{and} ~~ d = 10 $.	1
6648	Find $ S_{ 730 } $ ( sum of first $ 730 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	1
6649	Find $ S_{ 3650 } $ ( sum of first $ 3650 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	1
6650	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	1