X

ADVERTISEMENT

Table of contents:

Our online arithmetic calculator is an online tool that evaluates the number sequence, generated by inserting a constant value. It can be used to locate any sequence property such as the common difference, the first term, the number of the first n terms, or nth term.

Arithmetic sequence calculator is also known as an arithmetic series calculator.

An arithmetic sequence is a sequential representation of numbers in which the difference is always the same in each term. This difference can be positive or negative, and depending on the sign will lead to a positive or negative infinity sequence.

**Few examples:**

**2, 4, 6, 8, 10, 12, 14, 16…**

**5, 2, -1, -4, -7, -10, -13, -16...**

**60, 60.1, 60.2, 60.3, 60.4, 60.5...**

The sequence is called an increasing sequence if the common difference of an arithmetic series is positive. It will be called a decreasing sequence if the common difference is negative. If the common difference is zero, it will be a monotone sequence.

Formula to find sum of arithmetic sequence/progression is:

**S = n/2 × [2a₁ + (n - 1)d]**

Formula to find nth term is:

**a _{n} = a + (n - 1)d**

In this equation,

**a₁** is the first term of the sequence**,**

**a _{n}** is the nᵗʰ term of the sequence,

**d** is a common difference.

Calculate nth term and sum of arithmetic progression if there are **10** number of terms with first term of **3** and difference of **6**

**S = n/2 × [2a₁ + (n - 1)d]**

**S = 10/2 × [2(3) + (10 - 1) × 6]**

**S = 300**

**a _{n} = a + (n - 1)d**

**a _{n }= 3 + (10 - 1) × 6**

**a _{n} = 57**

To get arithmetic sequence, simply add common difference in first term. Then keep adding common difference in the previous number until you get the final number in sequence.

**a _{1} **

**a _{2} **

**a _{3} **

**a**_{4}** ***= a*_{3}* + d = 15 + 6 = 21*

**a**_{5}** ***= a*_{4}_{ }*+ d = 21 + 6 = 27*

**a**_{6}** ***= a*_{5}* + d = 27 + 6 = 33*

**a**_{7}_{ }*= a*_{6}* + d = 33 + 6 = 39*

**a**_{8}** ***= a*_{7}* + d = 39 + 6 = 45*

**a**_{9}** ***= a*_{8}* + d = 45 + 6 = 51*

**a**_{10}** ***= a*_{9}* + d = 51 + 6 = 57*

So, the sequence will be,

**9, 15, 21, 27, 33, 39, 45, 51, 57**