yCalculator

Number Sequence Calculator

Last updated: April 2026

Arithmetic sequence

Each term increases or decreases by a constant difference.

Sum of n terms

78

a_n = 3 + (n - 1) x 4

First term

3

Common diff

4

Term 6

23

Terms

3711151923
Step-by-step working
  1. Step 1: a_n = 3 + (n - 1) x 4.
  2. a_6 = 3 + 5 x 4 = 23.
  3. Step 2: S_6 = 6/2 x (3 + 23).
  4. S_6 = 3 x 26 = 78.
  5. Sequence: 3, 7, 11, 15, 19, 23.

Arithmetic vs geometric sequences

Arithmetic sequences add the same difference each time. Geometric sequences multiply by the same ratio each time. This difference changes how terms grow and how sums are calculated.

The Fibonacci sequence in nature

Fibonacci numbers appear in branching patterns, spiral arrangements, and growth models. The ratio of consecutive terms approaches the golden ratio as the sequence gets larger.

Series vs sequence

A sequence is an ordered list of numbers. A series is the sum of sequence terms. Some geometric series converge to a finite total, while arithmetic and many geometric series diverge as more terms are added.

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.

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