 # 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.

Formula:
an = a1 + (n - 1)d

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Arithmetic sequence calculator is an online tool that calculates:

1. Arithmetic Sequence
2. Nth term value
3. 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:

nth term = a + (n - 1)d

Formula to find sum of arithmetic progression is:

S = n/2 × [2a + (n - 1)d]

Where:

a refers to nᵗʰ term of the sequence,

d refers to common difference, and

a₁ refers to first term of the sequence.

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

Example:

Find nth term and sum of arithmetic sequence for 15 number of terms if first term is 5 and difference is 4.

Solution:

Step 1: Identify the values.

n = 15

a = 5

d = 4

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

nth term = a + (n - 1)d

= 5 + (15 - 1) × 4

= 61

nth term = 61

S = n/2 × [2a₁ + (n - 1)d]

S = 15/2 × [2(5) + (15 - 1) × 4]

S = 495

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.

a1 = 5

a2 = a1 + d = 5 + 4 = 9

a3 = a2 + d = 9 + 4 = 13

a4 = a3 + d = 13 + 4 = 17

a5 = a+ d = 17 + 4 = 21

a6 = a5 + d = 21 + 4 = 25

a= a6 + d = 25 + 4 = 29

a8 = a7 + d = 29 + 4 = 33

a9 = a8 + d = 33 + 4 = 37

a10 = a9 + d = 37 + 4 = 41

a11 = a10 + d = 41 + 4 = 45

a12 = a11 + d = 45 + 4 = 49

a13 = a12 + d = 49 + 4 = 53

a14 = a13 + d = 53 + 4 = 57

a15 = a14 + d = 57 + 4 = 61

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

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