1) Counting Numbers
Sequence: \(1,2,3,4,5,\dots\)
Rule: Add 1 each time. Next terms: 6,7,8.
2) Even Numbers
Sequence: \(2,4,6,8,10,\dots\)
Rule: Add 2. Next terms: 12,14,16.
3) Odd Numbers
Sequence: \(1,3,5,7,9,\dots\)
Rule: Add 2. Next terms: 11,13,15.
4) Multiples of 5
Sequence: \(5,10,15,20,25,\dots\)
Rule: Add 5. Next terms: 30,35,40.
5) Squares
Sequence: \(1,4,9,16,25,\dots\)
Rule: \(n^2\). Next terms: 36,49,64.
6) Cubes
Sequence: \(1,8,27,64,125,\dots\)
Rule: \(n^3\). Next terms: 216,343,512.
7) Triangular Numbers
Sequence: \(1,3,6,10,15,21,\dots\)
Rule: Sum of first \(n\) natural numbers. Next: 28,36,45.
8) Powers of 2
Sequence: \(1,2,4,8,16,32,\dots\)
Rule: Multiply by 2. Next terms: 64,128,256.
9) Powers of 3
Sequence: \(1,3,9,27,81,\dots\)
Rule: Multiply by 3. Next terms: 243,729,2187.
10) Fibonacci (Virahānka) Numbers
Sequence: \(1,2,3,5,8,13,21,\dots\)
Rule: Each term = sum of previous 2. Next: 34,55,89.
11) Multiples of 7
Sequence: \(7,14,21,28,35,\dots\)
Rule: Add 7. Next: 42,49,56.
12) Alternating +1, –1
Sequence: \(1,2,1,2,1,2,\dots\)
Rule: Repeats 1 and 2. Next: 1,2,1.
13) Double the Previous
Sequence: \(1,2,4,8,16,\dots\)
Same as powers of 2. Next: 32,64,128.
14) Halves
Sequence: \(128,64,32,16,8,4,\dots\)
Rule: Divide by 2. Next: 2,1,0.5.
15) Add 3, then 6, then 9, ...
Sequence: \(1,4,10,19,31,\dots\)
Differences increase by 3. Next: 46,64,85.
16) Squares of Even Numbers
Sequence: \(4,16,36,64,100,\dots\)
Rule: \((2n)^2\). Next: 144,196,256.
17) Squares of Odd Numbers
Sequence: \(1,9,25,49,81,\dots\)
Rule: \((2n-1)^2\). Next: 121,169,225.
18) Multiples of 9
Sequence: \(9,18,27,36,45,\dots\)
Rule: Add 9. Next: 54,63,72.
19) 2-digit Palindromes
Sequence: \(11,22,33,44,55,\dots\)
Rule: Same digit repeated. Next: 66,77,88,99.
20) Prime Numbers
Sequence: \(2,3,5,7,11,13,17,\dots\)
Rule: Numbers with no factors other than 1 and itself. Next: 19,23,29.