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Nth term of an AP

The nth term of an AP is the formula used to find any term directly without writing all the earlier terms.

In one line: First term plus one less set of jumps than the term number.

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Understand it

The nth term formula saves time in exams because it gives the required term in one step. For an AP with first term a and common difference d, the nth term is found by starting from the first term and adding the common difference one less time than the term number.

Formula and rule

an = a + (n - 1)d, where a is the first term, d is the common difference, and n is the term number.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1For the AP 2, 7, 12, 17, ... we have a = 2 and d = 5.
  2. 2The 6th term is a6 = 2 + (6 - 1)5 = 2 + 25 = 27.

Method you can reuse

  1. 1Identify the first term a.
  2. 2Find d.
  3. 3Put the required n into an = a + (n - 1)d.
  4. 4Simplify carefully.

Visual tip

A term ladder with labels a, a + d, a + 2d, a + 3d helps show why the formula uses n - 1 differences.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What formula is used to find the nth term of an AP?

Think first, then show answer
The nth term of an AP is an = a + (n - 1)d, where a is the first term and d is the common difference. This formula helps you find any term directly.

Common wrong answer

A common wrong answer is a + nd. That adds one extra difference and shifts every term forward.

Don't mix this up

Students often use n instead of n - 1, which gives one extra common difference.

Exam tip

Write the formula first, then substitute a, d, and n carefully before simplifying.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

CBSE often asks for a particular term, the position of a term, or a term in a sequence given as an AP.
  1. 1

    Enough for 1 mark

    The nth term of an AP is the formula used to find any term directly without writing all the earlier terms.

  2. 2

    Add for 2 marks

    Example: For 5, 9, 13, 17, ... the 4th term is 5 + 3(4 - 1) = 14.

  3. 3

    Add for 3 marks

    For an AP with first term a and common difference d, the nth term is found by starting from the first term and adding the common difference one less time than the term number.

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