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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.

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

    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. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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.

Example

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

Rule to remember

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

Memory hook

Position number tells you how many steps to count after the first term.

Examples and method

Worked example

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

Method to apply

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

Diagram support

A sequence line with the required term circled helps students connect the position number with the formula.

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.

Avoid common mistakes

Common confusion

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

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.

Exam tip

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

Quick check

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

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.

Answer writing and exam use

1-mark answer

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-mark answer

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. a_n = a + (n - 1)d is the direct rule for any specific term in an AP. In the AP 4, 9, 14, 19, ..., the 10th term is 4 + 9(5) = 49.

3-mark answer

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. a_n = a + (n - 1)d is the direct rule for any specific term in an AP. For 11, 15, 19, 23, ... the 12th term is 11 + (12 - 1)4 = 11 + 44 = 55. 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. A common wrong answer is to use the term number as the number of additions from zero, not from the first term.
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