Find The 30th 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 the 30th term of any arithmetic or geometric sequence with just a few inputs.

How to Use This Calculator

To find the 30th term of a sequence, you'll need to know whether it's arithmetic or geometric and provide the necessary starting values. Here's how to use our calculator:

Select the type of sequence (arithmetic or geometric)
Enter the first term of the sequence
For arithmetic sequences, enter the common difference
For geometric sequences, enter the common ratio
Click "Calculate" to see the 30th term

The calculator will display the result and show a chart of the sequence terms if you're using a geometric sequence.

The Formula Explained

There are two main types of sequences we can calculate:

Arithmetic Sequences

An arithmetic sequence has a constant difference between terms. The formula to find the nth term is:

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 3 and the common difference is 2, the 5th term would be:

a₅ = 3 + (5 - 1) × 2 = 3 + 8 = 11

Geometric Sequences

A geometric sequence has a constant ratio between terms. The formula to find the nth term is:

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 4th term would be:

a₄ = 2 × 3^(4 - 1) = 2 × 27 = 54

Worked Examples

Arithmetic Sequence Example

Find the 30th term of an arithmetic sequence where the first term is 5 and the common difference is 4.

a₃₀ = 5 + (30 - 1) × 4 a₃₀ = 5 + 29 × 4 a₃₀ = 5 + 116 a₃₀ = 121

Geometric Sequence Example

Find the 30th term of a geometric sequence where the first term is 3 and the common ratio is 2.

a₃₀ = 3 × 2^(30 - 1) a₃₀ = 3 × 2²⁹ a₃₀ = 3 × 536,870,912 a₃₀ = 1,610,612,736

Frequently Asked Questions

What's the difference between arithmetic and geometric sequences?

An arithmetic sequence has a constant difference between terms (like 2, 5, 8, 11), while a geometric sequence has a constant ratio between terms (like 3, 9, 27, 81).

Can I find terms beyond the 30th?

Yes, our calculator can find any term number you specify by changing the "Term number" input.

What if I don't know the first term or common difference/ratio?

You'll need this information to use our calculator. If you only have partial information, you might need to solve for the missing values first.