sequence
listlengths 5
7
| next_term
int64 7
4.78M
| explanation
stringlengths 54
134
| type
stringclasses 2
values |
|---|---|---|---|
[
1,
2,
6,
12,
16,
32,
36
] | 72 |
An alternating series starting at 1 that alternates between multiplying by 2 and adding 4.
|
Alternating
|
[
6,
11,
16,
21,
26,
31,
36
] | 41 |
Arithmetic Progression (AP) with parameters: {'start': 6, 'diff': 5}
|
Normal
|
[
2,
4,
8,
64,
68,
4624
] | 4,628 |
An alternating series starting at 2 that alternates between raising to the power of 2 and adding 4.
|
Alternating
|
[
5,
10,
20,
40,
80,
160,
320
] | 640 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 2}
|
Normal
|
[
5,
11,
33,
39,
117
] | 123 |
An alternating series starting at 5 that alternates between adding 6 and multiplying by 3.
|
Alternating
|
[
6,
27,
128,
629,
3130,
15631,
78132
] | 390,633 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 5}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
1,
4,
27,
256,
3125,
46656
] | 823,543 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
1,
4,
27,
256,
3125,
46656
] | 823,543 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
4,
16,
64,
256,
1024,
4096,
16384
] | 65,536 |
Geometric Progression (GP) with parameters: {'start': 4, 'ratio': 4}
|
Normal
|
[
5,
8,
31,
260,
3129,
46660
] | 823,547 |
Power Series (n^n) with parameters: {'base_offset': 1}, with a constant value of 4 added to each term.
|
Normal
|
[
1,
5,
25,
125,
625
] | 3,125 |
Geometric Progression (GP) with parameters: {'start': 1, 'ratio': 5}
|
Normal
|
[
5,
9,
36,
40,
160,
164
] | 656 |
An alternating series starting at 5 that alternates between adding 4 and multiplying by 4.
|
Alternating
|
[
4,
20,
100,
500,
2500,
12500
] | 62,500 |
Geometric Progression (GP) with parameters: {'start': 4, 'ratio': 5}
|
Normal
|
[
1,
1,
2,
4,
8,
64
] | 128 |
An alternating series starting at 1 that alternates between raising to the power of 2 and multiplying by 2.
|
Alternating
|
[
2,
6,
30,
260,
3130
] | 46,662 |
Power Series (n^n) with parameters: {'base_offset': 1}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
1,
1,
8,
64,
71
] | 5,041 |
An alternating series starting at 1 that alternates between raising to the power of 2 and adding 7.
|
Alternating
|
[
3,
7,
11,
15,
19,
23
] | 27 |
Arithmetic Progression (AP) with parameters: {'start': 3, 'diff': 4}
|
Normal
|
[
5,
15,
45,
135,
405,
1215,
3645
] | 10,935 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 3}
|
Normal
|
[
3,
9,
18,
324,
648
] | 419,904 |
An alternating series starting at 3 that alternates between raising to the power of 2 and multiplying by 2.
|
Alternating
|
[
6,
17,
48,
139,
410,
1221
] | 3,652 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 3}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
1,
1,
3,
9,
27,
729
] | 2,187 |
An alternating series starting at 1 that alternates between raising to the power of 2 and multiplying by 3.
|
Alternating
|
[
14,
30,
110,
510,
2510
] | 12,510 |
Geometric Progression (GP) with parameters: {'start': 4, 'ratio': 5}, with a constant value of 10 added to each term.
|
Normal
|
[
1,
4,
27,
256,
3125
] | 46,656 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
3,
10,
100,
107,
11449
] | 11,456 |
An alternating series starting at 3 that alternates between adding 7 and raising to the power of 2.
|
Alternating
|
[
4,
16,
17,
289,
290,
84100
] | 84,101 |
An alternating series starting at 4 that alternates between raising to the power of 2 and adding 1.
|
Alternating
|
[
4,
12,
21,
63,
72
] | 216 |
An alternating series starting at 4 that alternates between multiplying by 3 and adding 9.
|
Alternating
|
[
9,
15,
21,
27,
33,
39
] | 45 |
Arithmetic Progression (AP) with parameters: {'start': 9, 'diff': 6}
|
Normal
|
[
6,
9,
32,
261,
3130
] | 46,661 |
Power Series (n^n) with parameters: {'base_offset': 1}, with a constant value of 5 added to each term.
|
Normal
|
[
5,
25,
125,
625,
3125,
15625,
78125
] | 390,625 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 5}
|
Normal
|
[
11,
21,
31,
41,
51,
61,
71
] | 81 |
Arithmetic Progression (AP) with parameters: {'start': 10, 'diff': 9}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
2,
10,
100,
500,
250000
] | 1,250,000 |
An alternating series starting at 2 that alternates between multiplying by 5 and raising to the power of 2.
|
Alternating
|
[
2,
4,
12,
24,
32,
64
] | 72 |
An alternating series starting at 2 that alternates between multiplying by 2 and adding 8.
|
Alternating
|
[
1,
2,
8,
9,
729
] | 730 |
An alternating series starting at 1 that alternates between adding 1 and raising to the power of 3.
|
Alternating
|
[
2,
6,
30,
260,
3130
] | 46,662 |
Power Series (n^n) with parameters: {'base_offset': 1}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
4,
8,
16,
32,
64,
128
] | 256 |
Geometric Progression (GP) with parameters: {'start': 4, 'ratio': 2}
|
Normal
|
[
5,
25,
35,
175,
185,
925
] | 935 |
An alternating series starting at 5 that alternates between multiplying by 5 and adding 10.
|
Alternating
|
[
5,
11,
22,
28,
56,
62
] | 124 |
An alternating series starting at 5 that alternates between adding 6 and multiplying by 2.
|
Alternating
|
[
9,
17,
41,
113,
329,
977
] | 2,921 |
Geometric Progression (GP) with parameters: {'start': 4, 'ratio': 3}, with a constant value of 5 added to each term.
|
Normal
|
[
4,
8,
64,
68,
4624
] | 4,628 |
An alternating series starting at 4 that alternates between adding 4 and raising to the power of 2.
|
Alternating
|
[
2,
6,
30,
260,
3130
] | 46,662 |
Power Series (n^n) with parameters: {'base_offset': 1}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
5,
10,
40,
45,
180,
185,
740
] | 745 |
An alternating series starting at 5 that alternates between adding 5 and multiplying by 4.
|
Alternating
|
[
2,
6,
8,
24,
26,
78
] | 80 |
An alternating series starting at 2 that alternates between multiplying by 3 and adding 2.
|
Alternating
|
[
0,
2,
24,
252,
3120
] | 46,650 |
Power Series (n^n) with parameters: {'base_offset': 1}, with 'n' (the index starting from 1) subtracted from each term.
|
Normal
|
[
1,
4,
27,
256,
3125,
46656
] | 823,543 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
1,
1,
7,
49,
55,
3025
] | 3,031 |
An alternating series starting at 1 that alternates between raising to the power of 2 and adding 6.
|
Alternating
|
[
7,
11,
19,
35,
67,
131,
259
] | 515 |
Geometric Progression (GP) with parameters: {'start': 4, 'ratio': 2}, with a constant value of 3 added to each term.
|
Normal
|
[
4,
12,
20,
28,
36,
44
] | 52 |
Arithmetic Progression (AP) with parameters: {'start': 4, 'diff': 8}
|
Normal
|
[
1,
4,
27,
256,
3125
] | 46,656 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
4,
10,
40,
46,
184,
190
] | 760 |
An alternating series starting at 4 that alternates between adding 6 and multiplying by 4.
|
Alternating
|
[
1,
4,
27,
256,
3125
] | 46,656 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
1,
11,
22,
32,
64
] | 74 |
An alternating series starting at 1 that alternates between adding 10 and multiplying by 2.
|
Alternating
|
[
6,
14,
22,
30,
38,
46
] | 54 |
Arithmetic Progression (AP) with parameters: {'start': 6, 'diff': 8}
|
Normal
|
[
7,
9,
11,
13,
15,
17,
19
] | 21 |
Arithmetic Progression (AP) with parameters: {'start': 2, 'diff': 2}, with a constant value of 5 added to each term.
|
Normal
|
[
5,
7,
28,
30,
120
] | 122 |
An alternating series starting at 5 that alternates between adding 2 and multiplying by 4.
|
Alternating
|
[
6,
27,
128,
629,
3130,
15631
] | 78,132 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 5}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
4,
13,
42,
131,
400,
1209,
3638
] | 10,927 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 3}, with 'n' (the index starting from 1) subtracted from each term.
|
Normal
|
[
6,
9,
12,
15,
18,
21,
24
] | 27 |
Arithmetic Progression (AP) with parameters: {'start': 6, 'diff': 3}
|
Normal
|
[
5,
10,
100,
200,
40000
] | 80,000 |
An alternating series starting at 5 that alternates between multiplying by 2 and raising to the power of 2.
|
Alternating
|
[
1,
3,
8,
24,
29
] | 87 |
An alternating series starting at 1 that alternates between multiplying by 3 and adding 5.
|
Alternating
|
[
1,
8,
47,
246,
1245,
6244,
31243
] | 156,242 |
Geometric Progression (GP) with parameters: {'start': 2, 'ratio': 5}, with 'n' (the index starting from 1) subtracted from each term.
|
Normal
|
[
4,
8,
11,
22,
25
] | 50 |
An alternating series starting at 4 that alternates between multiplying by 2 and adding 3.
|
Alternating
|
[
10,
19,
28,
37,
46,
55
] | 64 |
Arithmetic Progression (AP) with parameters: {'start': 10, 'diff': 9}
|
Normal
|
[
1,
1,
3,
9,
27
] | 729 |
An alternating series starting at 1 that alternates between raising to the power of 2 and multiplying by 3.
|
Alternating
|
[
1,
5,
9,
13,
17,
21,
25
] | 29 |
Arithmetic Progression (AP) with parameters: {'start': 1, 'diff': 4}
|
Normal
|
[
3,
9,
27,
33,
99,
105
] | 315 |
An alternating series starting at 3 that alternates between adding 6 and multiplying by 3.
|
Alternating
|
[
3,
12,
21,
30,
39
] | 48 |
Arithmetic Progression (AP) with parameters: {'start': 3, 'diff': 9}
|
Normal
|
[
4,
12,
17,
51,
56
] | 168 |
An alternating series starting at 4 that alternates between multiplying by 3 and adding 5.
|
Alternating
|
[
1,
4,
27,
256,
3125,
46656
] | 823,543 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
7,
11,
15,
19,
23,
27,
31
] | 35 |
Arithmetic Progression (AP) with parameters: {'start': 7, 'diff': 4}
|
Normal
|
[
2,
6,
18,
54,
162
] | 486 |
Geometric Progression (GP) with parameters: {'start': 2, 'ratio': 3}
|
Normal
|
[
2,
6,
7,
21,
22,
66,
67
] | 201 |
An alternating series starting at 2 that alternates between multiplying by 3 and adding 1.
|
Alternating
|
[
5,
6,
7,
8,
9
] | 10 |
Arithmetic Progression (AP) with parameters: {'start': 5, 'diff': 1}
|
Normal
|
[
5,
7,
14,
16,
32,
34
] | 68 |
An alternating series starting at 5 that alternates between adding 2 and multiplying by 2.
|
Alternating
|
[
1,
2,
4,
8,
64,
128,
16384
] | 32,768 |
An alternating series starting at 1 that alternates between multiplying by 2 and raising to the power of 2.
|
Alternating
|
[
3,
15,
75,
375,
1875,
9375
] | 46,875 |
Geometric Progression (GP) with parameters: {'start': 3, 'ratio': 5}
|
Normal
|
[
5,
8,
31,
260,
3129
] | 46,660 |
Power Series (n^n) with parameters: {'base_offset': 1}, with a constant value of 4 added to each term.
|
Normal
|
[
3,
9,
27,
81,
243,
729
] | 2,187 |
Geometric Progression (GP) with parameters: {'start': 3, 'ratio': 3}
|
Normal
|
[
5,
25,
29,
841,
845
] | 714,025 |
An alternating series starting at 5 that alternates between raising to the power of 2 and adding 4.
|
Alternating
|
[
12,
14,
18,
26,
42
] | 74 |
Geometric Progression (GP) with parameters: {'start': 2, 'ratio': 2}, with a constant value of 10 added to each term.
|
Normal
|
[
5,
8,
31,
260,
3129
] | 46,660 |
Power Series (n^n) with parameters: {'base_offset': 1}, with a constant value of 4 added to each term.
|
Normal
|
[
1,
3,
9,
27,
81,
243
] | 729 |
Geometric Progression (GP) with parameters: {'start': 1, 'ratio': 3}
|
Normal
|
[
2,
4,
8,
64,
128
] | 16,384 |
An alternating series starting at 2 that alternates between raising to the power of 2 and multiplying by 2.
|
Alternating
|
[
2,
4,
12,
14,
42,
44
] | 132 |
An alternating series starting at 2 that alternates between adding 2 and multiplying by 3.
|
Alternating
|
[
4,
20,
23,
115,
118,
590,
593
] | 2,965 |
An alternating series starting at 4 that alternates between multiplying by 5 and adding 3.
|
Alternating
|
[
1,
4,
64,
67,
300763
] | 300,766 |
An alternating series starting at 1 that alternates between adding 3 and raising to the power of 3.
|
Alternating
|
[
4,
13,
22,
31,
40
] | 49 |
Arithmetic Progression (AP) with parameters: {'start': 5, 'diff': 10}, with 'n' (the index starting from 1) subtracted from each term.
|
Normal
|
[
8,
19,
30,
41,
52,
63
] | 74 |
Arithmetic Progression (AP) with parameters: {'start': 7, 'diff': 10}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
9,
10,
11,
12,
13,
14,
15
] | 16 |
Arithmetic Progression (AP) with parameters: {'start': 7, 'diff': 1}, with a constant value of 2 added to each term.
|
Normal
|
[
8,
9,
10,
11,
12,
13
] | 14 |
Arithmetic Progression (AP) with parameters: {'start': 8, 'diff': 1}
|
Normal
|
[
2,
4,
5,
25,
26
] | 676 |
An alternating series starting at 2 that alternates between raising to the power of 2 and adding 1.
|
Alternating
|
[
2,
6,
18,
54,
162,
486,
1458
] | 4,374 |
Geometric Progression (GP) with parameters: {'start': 2, 'ratio': 3}
|
Normal
|
[
6,
17,
48,
139,
410,
1221
] | 3,652 |
Geometric Progression (GP) with parameters: {'start': 5, 'ratio': 3}, with 'n' (the index starting from 1) added to each term.
|
Normal
|
[
8,
12,
16,
20,
24,
28
] | 32 |
Arithmetic Progression (AP) with parameters: {'start': 5, 'diff': 4}, with a constant value of 3 added to each term.
|
Normal
|
[
4,
8,
12,
16,
20
] | 24 |
Arithmetic Progression (AP) with parameters: {'start': 5, 'diff': 5}, with 'n' (the index starting from 1) subtracted from each term.
|
Normal
|
[
3,
12,
15,
60,
63
] | 252 |
An alternating series starting at 3 that alternates between multiplying by 4 and adding 3.
|
Alternating
|
[
4,
11,
44,
51,
204,
211,
844
] | 851 |
An alternating series starting at 4 that alternates between adding 7 and multiplying by 4.
|
Alternating
|
[
3,
8,
24,
29,
87,
92
] | 276 |
An alternating series starting at 3 that alternates between adding 5 and multiplying by 3.
|
Alternating
|
[
0,
2,
24,
252,
3120,
46650
] | 823,536 |
Power Series (n^n) with parameters: {'base_offset': 1}, with 'n' (the index starting from 1) subtracted from each term.
|
Normal
|
[
1,
4,
27,
256,
3125,
46656
] | 823,543 |
Power Series (n^n) with parameters: {'base_offset': 1}
|
Normal
|
[
1,
5,
25,
125,
625,
3125
] | 15,625 |
Geometric Progression (GP) with parameters: {'start': 1, 'ratio': 5}
|
Normal
|
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