Free Maths Calculator

Nth Term Calculator

Type the first few terms of a sequence and get the nth term rule, for both linear sequences and quadratic ones with changing differences. The calculator shows the difference pattern, builds the rule from it, then checks the rule against your terms, which is exactly the working examiners award.

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Answer

Method, Step by Step

    Worked Example

    Find the nth term of 5, 8, 11, 14.

    1. Differences: +3, +3, +3. Constant, so it is linear and built on 3n
    2. At n = 1, 3n gives 3, but the first term is 5, so add 2
    3. The nth term is 3n + 2. Check n = 4:3 × 4 + 2 = 14 ✓

    Answer: 3n + 2

    Try These Yourself

    Find the nth term of 7, 12, 17, 22.Show answerHide answer

    Answer: 5n + 2

    Differences of +5, and 5 × 1 = 5 needs + 2 to reach 7.

    Find the nth term of 20, 17, 14, 11.Show answerHide answer

    Answer: −3n + 23

    Differences of −3, and −3 + 23 = 20.

    Find the nth term of 2, 8, 18, 32.Show answerHide answer

    Answer: 2n²

    Second differences are 4, so 2n², and the leftover is zero.