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# Arithmetic Sequence Calculator

Enter the values in the below input boxes to calculate the nth term and sum of arithmetic progression by using arithmetic sequence/series calculator.

## Arithmetic Sequence Solver

Arithmetic sequence calculator is an online tool that calculates:

- Arithmetic Sequence
- Nth term value
- Sum of arithmetic sequence

**What is an arithmetic sequence?**

Arithmetic sequence can be defined as,

**“**An arithmetic sequence is a sequence where each term increases by adding or subtracting some constant value known as common difference ** (d)**.

**”**

Arithmetic sequence is commonly known as arithmetic series and arithmetic progression as well.

**Arithmetic sequence formula**

Formula to find nth term is:

**n ^{th} term = a + (n - 1)d**

Formula to find sum of arithmetic progression is:

**S = n/2 × [2a****₁**** + (n - 1)d]**

Where:

refers to nᵗʰ term of the sequence,*a*refers to common difference, and*d*refers to first term of the sequence.*a₁*

There is no specific formula to find arithmetic sequence. In the next section, we will explain the method to calculate arithmetic sequence using common difference and first term.

**Finding nth term, arithmetic sequence and its sum**

For the calculation of nth term, arithmetic sequence and its sum, you can simply use the arithmetic series calculator above.

*Example:*

Find the nth term and sum of arithmetic sequence for ** 15** number of terms if first term is

**and difference is**

*5*

*4.**Solution:*

**Step 1: **Identify the values.

n = 15

a = 5

d = 4

**Step 2: **Use arithmetic sequence formula and place the values.

**For finding the nth term**

**n ^{th} term = a + (n - 1)d**

= 5 + (15 - 1) × 4

= 61

n^{th} term = 61

**For finding the sum of arithmetic sequence**

**S = n/2 × [2a₁ + (n - 1)d]**

*S = 15/2 × [2(5) + (15 - 1) × 4]*

*S = 495*

*For finding the Arithmetic Sequence*

Add common difference in the first term to get the arithmetic sequence. Keep adding the common difference in the preceding number till you get last number in the sequence.

a_{1} = 5

a_{2} = a_{1} + d = 5 + 4 = 9

a_{3} = a_{2} + d = 9 + 4 = 13

a_{4} = a_{3} + d = 13 + 4 = 17

a_{5} = a_{4 }+ d = 17 + 4 = 21

a_{6} = a_{5} + d = 21 + 4 = 25

a_{7 }= a_{6} + d = 25 + 4 = 29

a_{8} = a_{7} + d = 29 + 4 = 33

a_{9} = a_{8} + d = 33 + 4 = 37

a_{10} = a_{9} + d = 37 + 4 = 41

a_{11} = a10 + d = 41 + 4 = 45

a_{12} = a11 + d = 45 + 4 = 49

a_{13} = a12 + d = 49 + 4 = 53

a_{14} = a13 + d = 53 + 4 = 57

a_{15} = a14 + d = 57 + 4 = 61

**Arithmetic Sequence =** **9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61**

Use the arithmetic progression calculator above to verify the value of nth term and arithmetic sequence.