Contents

- 1 What is a series and a sequence?
- 2 What is a series?
- 3 How do you find a series?
- 4 What are the two types of series?
- 5 What is a sum of a series?
- 6 What do you call a series of series?
- 7 What is the limit of a series?
- 8 What is the series formula?
- 9 How do you answer a series number?
- 10 How do you solve series and sequence problems?

## What is a series and a sequence?

In mathematics, a sequence is a list of objects (or events) which have been ordered in a sequential fashion; such that each member either comes before, or after, every other member. A series is a sum of a sequence of terms. That is, a series is a list of numbers with addition operations between them.

## What is a series?

noun, plural se·ries. a group or a number of related or similar things, events, etc., arranged or occurring in temporal, spatial, or other order or succession; sequence. a number of games, contests, or sporting events, with the same participants, considered as a unit: The two baseball clubs played a five-game series.

## How do you find a series?

The series of a sequence is the sum of the sequence to a certain number of terms. It is often written as S_{n}. So if the sequence is 2, 4, 6, 8, 10, , the sum to 3 terms = S_{3} = 2 + 4 + 6 = 12.

## What are the two types of series?

Series: Types of Series and Types of Tests

- Types of Series.
- Harmonic Series: This is an example of divergent series.
- Geometric Series: Geometric Series is a series where the ratio of each two consecutive terms is a constant function of the summation index.
- P- Series: P- series is a series where the common exponent p is a positive real constant number.

## What is a sum of a series?

The sum of the terms of a sequence is called a series. If a sequence is arithmetic or geometric there are formulas to find the sum of the first n terms, denoted Sn, without actually adding all of the terms.

## What do you call a series of series?

Multi-volume works are usually called a series. Some people call a set of two a duology, and a set of four a quadrilogy, but the trilogy is so very much more common than a set of two, or four (or more) that ‘trilogy’ is well known. A series of books with four or more is usually called just a ‘ series ‘.

## What is the limit of a series?

The limit of a series is the value the series ‘ terms are approaching as n → ∞ ntoinfty n→∞. The sum of a series is the value of all the series ‘ terms added together.

## What is the series formula?

The sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ). It is called the arithmetic series formula.

## How do you answer a series number?

You can find the right answer in number series by taking the difference between consecutive pairs of numbers, which form a logical series. In this example, the differences between succeeding pairs of numbers are 1,2, 4, 8, 16, and 32. So, the next difference must be 64.

## How do you solve series and sequence problems?

The formulae for sequence and series are:

- The n
^{th}term of the arithmetic sequence or arithmetic progression (A.P) is given by a_{n}= a + (n – 1) d. - The arithmetic mean [A.M] between a and b is A.M = [a + b] / 2.
- The n
^{th}term an of the geometric sequence or geometric progression [G.P] is a_{n}= a * r.