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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 calculator is an online tool that calculates the sum of arithmetic sequence and nth term for the given values.

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 Nth term

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.

Finding nth term and sum of arithmetic sequence

Example:

Find nth term and sum of arithmetic sequence for 100 number of terms if first term is 5 and difference is 4.

Solution:

Step 1: Identify the values.

n = 100

a = 5

d = 4

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

nth term = a + (n - 1)d

= 5 + (100 - 1) × 4

= 5 + (100 - 1) × 4

nth term = 401

S = n/2 × [2a₁ + (n - 1)d]

S = 100/2 × [2(5) + (100 - 1) × 4]

S = 20,300

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


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