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
1	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	101
2	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	84
3	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	70
4	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	63
5	$$ a_1 = -6 ~,~ d = 2 ~,~ S_n = -10 ~,~ n = ? $$	46
6	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	44
7	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	41
8	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	39
9	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	38
10	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	36
11	Find $ a_1 $ (first term of arithmetic progression) if $ d = \frac{ 4 }{ 3 } ~~ \text{and} ~~ a_{ 8 } = 5 $.	31
12	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	30
13	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	29
14	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	26
15	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	26
16	Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	25
17	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	24
18	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	23
19	Find $ a_{ 365 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	23
20	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	22
21	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 4 $.	22
22	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 7 $.	22
23	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	22
24	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	22
25	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	21
26	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -5 \right) $.	21
27	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = -10 $.	21
28	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	21
29	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	21
30	$$ a_{ 12 } = 15 ~~,~~ S_{ 9 } = 55 ~~,~~ a_1 = ? ~~,~~ d = ? $$	20
31	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	20
32	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = \left( -10 \right) $.	20
33	Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	20
34	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	20
35	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	20
36	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	20
37	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	19
38	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	19
39	Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 4 $.	19
40	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	19
41	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -5 \right) $.	19
42	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	18
43	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	18
44	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	18
45	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 10 $.	18
46	$$ a_1 = -12 ~,~ d = 3 ~,~ S_n = 1104 ~,~ n = ? $$	17
47	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = 7 $.	17
48	Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 6 $.	17
49	Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 16 $.	17
50	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -21 ~~ \text{and} ~~ d = 7 $.	16