Find The Nth Term of The Following Sequence Calculator

Finding the nth term of a sequence is a fundamental math skill used in algebra, physics, and computer science. This calculator helps you determine any term in an arithmetic or geometric sequence quickly and accurately.

How to Use This Calculator

To find the nth term of a sequence:

Select whether your sequence is arithmetic or geometric.
Enter the first term of the sequence.
Enter the common difference (for arithmetic) or common ratio (for geometric).
Enter the term number (n) you want to find.
Click "Calculate" to see the result.

The calculator will display the nth term along with a clear explanation of how it was calculated.

Arithmetic Sequences

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This difference is called the common difference (d).

Arithmetic Sequence Formula

The nth term of an arithmetic sequence can be found using:

aₙ = a₁ + (n - 1) × d

Where:

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

For example, if the first term is 5 and the common difference is 3, the sequence would be: 5, 8, 11, 14, 17, ...

Geometric Sequences

A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio (r).

Geometric Sequence Formula

The nth term of a geometric sequence is calculated with:

aₙ = a₁ × r^(n - 1)

Where:

aₙ = nth term
a₁ = first term
r = common ratio
n = term number

For example, if the first term is 2 and the common ratio is 3, the sequence would be: 2, 6, 18, 54, 162, ...

Worked Examples

Arithmetic Sequence Example

Find the 7th term of an arithmetic sequence where the first term is 4 and the common difference is 5.

Using the formula: a₇ = 4 + (7 - 1) × 5 = 4 + 30 = 34

The 7th term is 34.

Geometric Sequence Example

Find the 5th term of a geometric sequence where the first term is 3 and the common ratio is 2.

Using the formula: a₅ = 3 × 2^(5 - 1) = 3 × 16 = 48

The 5th term is 48.

Frequently Asked Questions

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.

How do I know if a sequence is arithmetic or geometric?

Check if the difference between consecutive terms is constant (arithmetic) or if the ratio between consecutive terms is constant (geometric).

Can I use negative numbers in these sequences?

Yes, the calculator accepts both positive and negative numbers for terms, differences, and ratios.

What if the common ratio is zero?

If the common ratio is zero, all terms after the first will be zero.