medium difficulty5 min

Finding a specific term in an AP

Finding a specific term means locating the required term number in an AP using the nth-term formula or by working backward from the sequence.

In one line: Position number tells you how many steps to count after the first term.

Practice This Concept

Understand it

Many exam questions do not ask for the entire AP. They ask for a particular term such as the 10th term, 25th term, or a term that matches a given value. The safest method is to use the nth-term formula and substitute the right values carefully.

Example

In the AP 4, 9, 14, 19, ..., the 10th term is 4 + 9(5) = 49.

Formula and rule

a_n = a + (n - 1)d is the direct rule for any specific term in an AP.

See it worked out

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

Worked example

For 11, 15, 19, 23, ... the 12th term is 11 + (12 - 1)4 = 11 + 44 = 55.

Method you can reuse

1Note the first term and common difference.
2Write the nth-term formula.
3Substitute the required n.
4Simplify the arithmetic carefully.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

How do you find a specific term in an AP quickly?

Think first, then show answer

Use the nth-term formula a_n = a + (n - 1)d and substitute the term number directly. This gives the required term without listing all earlier terms.

Common wrong answer

A common wrong answer is to use the term number as the number of additions from zero, not from the first term.

Don't mix this up

Students sometimes stop at the third or fourth term instead of using the formula for the exact required position.

Exam tip

When the question asks for a specific term, do not write the whole list unless it helps you check your formula.

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

Questions may ask for the n-th term, the term at a given position, or the value of n when a certain term is known.

1
Enough for 1 mark
Finding a specific term means locating the required term number in an AP using the nth-term formula or by working backward from the sequence.
2
Add for 2 marks
Example: In the AP 4, 9, 14, 19, ..., the 10th term is 4 + 9(5) = 49.
3
Add for 3 marks
They ask for a particular term such as the 10th term, 25th term, or a term that matches a given value.

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