C
CraftExam
medium difficulty5 min

Middle term in an AP

The middle term of an AP is the term that lies exactly between two equal numbers of terms on both sides.

In one line: Middle means same number of terms on both sides.

Practice This Concept

Understand it

When the number of terms in an AP is odd, the middle term is the term at the center. In a well-balanced AP, the middle term is also the average of the first and last terms when the terms are arranged symmetrically.

Example

In 2, 5, 8, 11, 14, the middle term is 8.

Formula and rule

For an AP with an odd number of terms, middle term = an+1/2.

See it worked out

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

Worked example

In 4, 7, 10, 13, 16, 19, 22, there are 7 terms, so the 4th term is the middle term, which is 13.

Method you can reuse

  1. 1Count the total terms.
  2. 2Check whether the count is odd.
  3. 3Find the central position using (n + 1)/2.
  4. 4Read that term from the AP.

Sketch it in your answer

Write the terms in a row and mark equal terms on both sides of the center.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

How do you find the middle term of an AP with an odd number of terms?

Think first, then show answer
Count the total number of terms and choose the central term. For an odd number of terms, the middle term is the one with equal terms on both sides.

Common wrong answer

A common wrong answer is to pick the term in the center by appearance without counting all the terms carefully.

Don't mix this up

Students sometimes call the third term the middle term without checking whether the sequence has an odd number of terms.

Exam tip

First count the total number of terms. Only then decide which one is in the middle.

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

Students may be asked to identify the central term or use the middle term in relation to the first and last terms.
  1. 1

    Enough for 1 mark

    The middle term of an AP is the term that lies exactly between two equal numbers of terms on both sides.

  2. 2

    Add for 2 marks

    Example: In 2, 5, 8, 11, 14, the middle term is 8.

  3. 3

    Add for 3 marks

    When the number of terms in an AP is odd, the middle term is the term at the center.

MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept