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Explicit Formula Calculator

Enter your sequence and click on the “CALCULATE” button to get an instant and accurate solution.

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The sequence 10, 20, 30, 40,... follows an arithmetic pattern. Determine the explicit formula for the nth term of this sequence. Then, use the formula to find the 25th term of the sequence.

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Explicit Formula Calculator

Use the Explicit Formula Calculator to quickly find the nth term of any arithmetic or geometric sequence. Enter the first term, common difference or ratio, and the position n, and get the exact value instantly.

What is an Explicit Formula?

An explicit formula allows you to calculate any term in a sequence directly, without needing the previous terms. It expresses the nth term as a function of its position n.

Formulas

Arithmetic Sequence:

aₙ = a₁ + (n − 1) · d

Geometric Sequence:

aₙ = a₁ · r⁽ⁿ⁻¹⁾

Steps to Solve Explicit Sequences

Determine the sequence type: arithmetic or geometric.
Identify the first term (a₁).
Find the common difference (d) or common ratio (r).
Specify the term number (n).
Substitute the values into the explicit formula and calculate the term.

Example:

Find the 8th term of the arithmetic sequence: 3, 6, 9, 12,...

Given:

First term: a₁ = 3
Common difference: d = 3
Term number: n = 8

Solution:

Step 1: Identify the sequence type → Arithmetic

Arithmetic formula: aₙ = a₁ + (n − 1) · d

Step 2: Substitute values

a₈ = 3 + (8 − 1) · 3

Step 3: Simplify

a₈ = 3 + 7 · 3 = 3 + 21 = 24

✅ Answer: The 8th term is 24.

You can also use the Explicit Formula Calculator to get results instantly for both arithmetic and geometric sequences.

How the Calculator Works

Choose Sequence Type: Arithmetic or geometric.
Enter First Term (a₁): Input the first number of the sequence.
Enter Common Difference (d) or Ratio (r): Provide the progression value.
Enter Term Number (n): Specify the term to calculate.
Click Calculate: The result is displayed instantly.

Benefits of Using the Explicit Formula Calculator

Efficient for Large Sequences: Saves time when calculating high-term positions.
Accurate: Reduces calculation errors.
User-Friendly: Simple interface with immediate results.
Supports Learning: Step-by-step calculations help students understand sequences.
Responsive: Works on mobile, tablet, and desktop devices.