An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant. In other words, each term is obtained by adding a fixed number to the previous term. The formula to find the nth term of an arithmetic series is given by:

nth term (an) = a1 + (n - 1)d

Where:
- a1 is the first term of the series
- n is the position of the term in the series
- d is the common difference between each term

Example: 2, 5, 8, 11, 14, ...



A geometric series is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number called the common ratio (r). The formula to find the nth term of a geometric series is given by:

nth term (an) = a1 * r^(n-1)

Where:
- a1 is the first term of the series
- r is the common ratio between each term
- n is the position of the term in the series

Example: 3, 6, 12, 24, 48, ...



The harmonic series is a sequence of numbers in which each term is the reciprocal of a positive integer. The formula to find the nth term of a harmonic series is given by:

nth term (an) = 1/n

Where:
- n is the position of the term in the series

Example: 1, 1/2, 1/3, 1/4, 1/5, ...



The Fibonacci series is a sequence of numbers in which each term is the sum of the two preceding terms. The series starts with 0 and 1, and each subsequent term is obtained by adding the two previous terms. The formula to find the nth term of a Fibonacci series is given by:

nth term (an) = a(n-1) + a(n-2)

Where:
- a0 and a1 are the first two terms of the series
- n is the position of the term in the series

Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...



- Arithmetic series: Each term is obtained by adding a fixed number to the previous term.
- Geometric series: Each term is obtained by multiplying the previous term by a fixed number (common ratio).
- Harmonic series: Each term is the reciprocal of a positive integer.
- Fibonacci series: Each term is the sum of the two preceding terms.