Find N Term Calculator

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This calculator helps you find any term in an arithmetic sequence using the first term and common difference.

What is Find n Term?

The Find n Term calculator determines the value of any term in an arithmetic sequence. An arithmetic sequence is a sequence of numbers where each term after the first is obtained by adding a constant difference to the preceding term.

Key Concepts

First term (a₁): The starting value of the sequence
Common difference (d): The constant amount added between terms
Term number (n): The position of the term you want to find

When to Use This Calculator

This calculator is useful in various fields including:

Mathematics education
Physics problems involving uniform motion
Financial calculations with equal payments
Any situation requiring prediction of future values based on a constant rate of change

How to Use the Calculator

Enter the first term (a₁) of your arithmetic sequence
Enter the common difference (d) between terms
Enter the term number (n) you want to find
Click "Calculate" to see the result
Review the detailed explanation of the calculation

Tip: For sequences that don't start at term 1, you can adjust the term number accordingly. For example, if your sequence starts at term 5, enter 5 as the term number to find the first term of your sequence.

Formula

The formula for finding the nth term of an arithmetic sequence is:

aₙ = a₁ + (n - 1) × d

Where:

aₙ = nth term
a₁ = first term
d = common difference
n = term number

The formula works by starting with the first term and then adding the common difference multiplied by (n-1) to get to the desired term. This accounts for all the steps needed to reach the nth term from the first.

Worked Example

Let's find the 8th term of an arithmetic sequence where the first term is 3 and the common difference is 4.

Identify the values: a₁ = 3, d = 4, n = 8
Plug the values into the formula: a₈ = 3 + (8 - 1) × 4
Calculate the multiplication: (8 - 1) × 4 = 7 × 4 = 28
Add to the first term: 3 + 28 = 31
Result: The 8th term is 31

Arithmetic Sequence Example
Term Number (n)	Term Value (aₙ)
1	3
2	7
3	11
4	15
5	19
6	23
7	27
8	31

As shown in the table, each term increases by 4, demonstrating the constant difference in an arithmetic sequence.

FAQ

What is the difference between arithmetic and geometric sequences?: An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms. For example, 2, 5, 8 is arithmetic, while 3, 9, 27 is geometric.
Can I use negative numbers in the calculator?: Yes, the calculator accepts negative values for the first term, common difference, and term number. This allows you to work with sequences that decrease over time.
What if I enter a term number that's not an integer?: The calculator will still perform the calculation, but the result may not correspond to a term in a traditional sequence. For most practical purposes, term numbers are whole numbers.
How can I verify the calculator's results?: You can manually apply the formula using the values you entered, or use the worked example as a reference. The calculator provides a detailed explanation of each step.