# Learn about the Arithmetic sequence and Arc length

- July 8, 2020
- 0

**What does it mean by sequence?**

A sequence is a set of things that come in order. The sequence is regular order in the series and each number in the sequence is called series. Let’s consider some examples to understand the concept.

Here are a few lists of numbers:

1, 2, 8, 9, 0, 3…

0, 0, 8, 7, 2, 1…

The above series of numbers cannot be considered as a sequence. Because each “term” in this group does not come in series and they have formed an irregular pattern. Let’s check another series of numbers.

1, 3, 5, 7, 9…

2, 4, 6, 8, 10…

4, 8, 12, 16, 20…

The above series represents a sequence in which each number follows a specific pattern. In set 1, there is a series of odd numbers. In the next group, there is a series of even numbers. Each term in the group came in a sequence.

The sequence always comes in the pattern in which we can easily predict the next number in series. Considering the above example, in a group one, it is confirmed that the next number in the series will be 11.

**What is the arithmetic sequence?**

An arithmetic sequence is a specific type of sequence in which the difference between one term and the other is constant. Arithmetic mean is written as:

**{A, a+d, a+2d, a+3d,}**

In the above expression, a is the first term, and d is the difference between terms in a sequence which is called the common difference. The arithmetic sequence is also termed as arithmetic progression.

And the difference between consecutive terms always remains the same. For example, in the sequence 1, 3, 5, 7, 9… the difference between the terms is two and it is continuous up to infinity.

Arithmetic sequence for the nth term will be:

**an=a1+ (n–1) d**

The above formula is used to calculate the arithmetic sequence for the nth term. It is the most basic and precise form of sequence. But the ambiguity lies when the complexity of numbers increases. In such a case you can use the arithmetic series calculator and get the results without any hustle.

**What is arc length?**

Arc length is the distance between two points in a section of the curve. The length of the arc could not be confused with the associate degree of an arc which represents the degree size of its central angle. Whereas arc length is the measurement of distance along the arc. Arc length is usually longer than the straight line. Measures the distance between its endpoints.

**How to find the arc length?**

The circle is equal to 3600 and it is divided into consecutive parts of 360 degrees. If the arc length is divided by 360 degrees then it comes to the fraction of the circle’s circumference which makes the arc.

**Arc length=s=rθ**

**What is the Arc length formula (Degree?)**

The formula for calculating arc length by using the length of the arc is:

**Arc length=2πR****∗****C360Arc length=2πR****∗****C360**

From the above expression, C is the central angle of the arc (degree), R shows the radius of the circle, π is a constant value which approximately equals to 3.142. The circumference of the circle is 2πR. Hence the arc length formula reduces this by dividing the angle of arc to 360 degrees. The above formula is used to find the central angle, radius, or arc length. If you know any of the above values you can find the arc length very easily. Moreover, the arc length formula in radians can be calculated from:

**Arc length=R****∗****Carc length=R****∗****C**

In which C represents the central angle of the arc in radians and R represents the radius of the arc. This formula is different from the arc length in degrees. In degrees, the 2π/360 converts the degree to radians.

And one radian is approximately equal to 57.30.

Arc length formula is easy to use and apply in algebraic operations. But the arc length can also be calculated from the arc length calculator in terms of pi.