C
CraftExam
high importancemedium8 min

Explicit (Direct) Rule for a Sequence

An explicit rule gives the value of any term directly using its position number n.

Practice This Concept

Learn the concept

Student-friendly explanation

If a sequence has a rule like an = 2n + 1, we can find the 10th term by putting n = 10 without listing all previous terms. This is useful when the question asks for a far-away term such as the 50th term.

How to write this in exams

  1. 1

    Start with the exact idea

    An explicit rule gives the value of any term directly using its position number n.

  2. 2

    Then show how to use it

    Identify the given rule. Note the required position. Substitute n carefully. Simplify using correct order of operations. Write the term with its position.

  3. 3

    Add one concrete example

    For an = 3n + 2, the 5th term is a5 = 3(5) + 2 = 17.

  4. 4

    Avoid this incomplete answer

    For an = 4n - 3, the 12th term is sometimes written as 4 + 12 - 3 = 13, which is wrong because multiplication by n was ignored.

Definition

An explicit rule gives the value of any term directly using its position number n.

Example

For an = 3n + 2, the 5th term is a5 = 3(5) + 2 = 17.

Rule to remember

Explicit form: an = expression in n. Here n is a natural number showing the term position.

Memory hook

Direct rule means jump straight to the term.

Examples and method

Worked example

Find the 12th term of an = 4n - 3. Put n = 12, so a12 = 4(12) - 3 = 48 - 3 = 45.

Method to apply

Identify the given rule. Note the required position. Substitute n carefully. Simplify using correct order of operations. Write the term with its position.

Diagram support

A two-column table with n and an can show how position values generate sequence terms.

How CBSE asks it

Questions may ask students to find a specific term, complete a table of n and an, or check whether a given number can be a term.

Avoid common mistakes

Common confusion

Students sometimes substitute the term value in place of n, but n represents the position, not the term itself.

Common wrong answer

For an = 4n - 3, the 12th term is sometimes written as 4 + 12 - 3 = 13, which is wrong because multiplication by n was ignored.

Exam tip

Before substituting, write what n means: n = required position number.

Quick check

For an = 2n + 1, what is the 6th term?

The 6th term is 13 because substituting n = 6 gives a6 = 2(6) + 1 = 13.

Study the explicit (direct) rule for a sequence diagram carefully

Use the labelled diagram to keep explicit (direct) rule for a sequence clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of explicit (direct) rule for a sequence in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on explicit (direct) rule for a sequence.

Revision cue

Revise explicit (direct) rule for a sequence through the labels before writing the answer.

Answer writing and exam use

1-mark answer

An explicit rule gives the value of any term directly using its position number n.

2-mark answer

An explicit rule gives the value of any term directly using its position number n. Explicit form: an = expression in n. Here n is a natural number showing the term position. For an = 3n + 2, the 5th term is a5 = 3(5) + 2 = 17.

3-mark answer

If a sequence has a rule like an = 2n + 1, we can find the 10th term by putting n = 10 without listing all previous terms. This is useful when the question asks for a far-away term such as the 50th term. Explicit form: an = expression in n. Here n is a natural number showing the term position. Find the 12th term of an = 4n - 3. Put n = 12, so a12 = 4(12) - 3 = 48 - 3 = 45. Questions may ask students to find a specific term, complete a table of n and an, or check whether a given number can be a term. For an = 4n - 3, the 12th term is sometimes written as 4 + 12 - 3 = 13, which is wrong because multiplication by n was ignored.
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