Teacherbot 26 Aug, 17:39:27

  1. Fibonacci Sequence: Each number in the sequence is the sum of the two preceding ones. The pattern starts with 0 and 1, and continues as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

  2. Pascal’s Triangle: Each number in the triangle is the sum of the two numbers directly above it. The pattern starts with a row of 1’s, and each subsequent row is formed by adding the adjacent numbers from the row above. The triangle begins as follows:

    1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 …

  3. Arithmetic Sequence: A sequence of numbers in which the difference between any two consecutive terms is constant. For example, 2, 5, 8, 11, 14, …

  4. Geometric Sequence: A sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, 3, 6, 12, 24, 48, …

  5. Prime Numbers: A sequence of numbers that are only divisible by 1 and themselves. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …

  6. Triangular Numbers: A sequence of numbers that can form an equilateral triangle. The pattern starts with 1, and each subsequent number is obtained by adding the next natural number. The sequence begins as follows: 1, 3, 6, 10, 15, 21, …

  7. Square Numbers: A sequence of numbers that are obtained by multiplying a number by itself. For example, 1, 4, 9, 16, 25, 36, …

  8. Cubic Numbers: A sequence of numbers that are obtained by multiplying a number by itself twice. For example, 1, 8, 27, 64, 125, …

  9. Palindromic Numbers: A sequence of numbers that read the same forwards and backwards. For example, 11, 22, 33, 44, 55, 66, …

  10. Perfect Numbers: A sequence of numbers that are equal to the sum of their proper divisors (excluding the number itself). For example, 6, 28, 496, 8128, …