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Real-World Applications of Sequences

Real-world applications of sequences use ordered patterns to model repeated changes in money, distance, growth, decay, arrangements, or daily-life quantities.

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Student-friendly explanation

Many word problems become easier when we first decide whether the change is by repeated addition or repeated multiplication. Fixed salary increase usually forms an AP. Repeated doubling, percentage growth, or halving often forms a GP.

How to write this in exams

  1. 1

    Start with the exact idea

    Real-world applications of sequences use ordered patterns to model repeated changes in money, distance, growth, decay, arrangements, or daily-life quantities.

  2. 2

    Then show how to use it

    Read the story carefully. Identify the first value. Decide if the change is fixed addition or fixed multiplication. Choose AP or GP. Substitute into the correct formula. Interpret the answer with units.

  3. 3

    Add one concrete example

    If a shopkeeper adds Rs 500 to monthly savings every month, it is AP. If a population doubles every hour, it is GP.

  4. 4

    Avoid this incomplete answer

    For fixed monthly increase, some students multiply by the increase and make it GP, but equal addition means AP.

Definition

Real-world applications of sequences use ordered patterns to model repeated changes in money, distance, growth, decay, arrangements, or daily-life quantities.

Example

If a shopkeeper adds Rs 500 to monthly savings every month, it is AP. If a population doubles every hour, it is GP.

Rule to remember

AP model: an = a + (n - 1)d. GP model: an = a · r^(n - 1). Use AP for equal addition and GP for equal multiplication.

Memory hook

Same add means AP; same multiply means GP.

Examples and method

Worked example

A student saves Rs 200 in January and increases savings by Rs 50 each month. The sixth month saving is a6 = 200 + 5(50) = Rs 450, so the model is AP.

Method to apply

Read the story carefully. Identify the first value. Decide if the change is fixed addition or fixed multiplication. Choose AP or GP. Substitute into the correct formula. Interpret the answer with units.

Diagram support

A comparison table with columns situation, type of change, AP or GP can help students classify word problems.

How CBSE asks it

Exam questions may describe salaries, savings, seating rows, tile patterns, population growth, or repeated discount and ask for a term or total.

Avoid common mistakes

Common confusion

Students often start calculating without deciding whether the situation uses a constant difference or a constant ratio.

Common wrong answer

For fixed monthly increase, some students multiply by the increase and make it GP, but equal addition means AP.

Exam tip

Underline the phrase showing change: fixed increase suggests AP; multiplied by the same factor suggests GP.

Quick check

A plant's height increases by 3 cm every week. Should it be modelled as AP or GP?

It should be modelled as an AP because the same amount, 3 cm, is added each week.

Study the real-world applications of sequences diagram carefully

Use the labelled diagram to keep real-world applications of sequences clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of real-world applications of sequences in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on real-world applications of sequences.

Revision cue

Revise real-world applications of sequences through the labels before writing the answer.

Answer writing and exam use

1-mark answer

Real-world applications of sequences use ordered patterns to model repeated changes in money, distance, growth, decay, arrangements, or daily-life quantities.

2-mark answer

Real-world applications of sequences use ordered patterns to model repeated changes in money, distance, growth, decay, arrangements, or daily-life quantities. AP model: an = a + (n - 1)d. GP model: an = a · r^(n - 1). Use AP for equal addition and GP for equal multiplication. If a shopkeeper adds Rs 500 to monthly savings every month, it is AP. If a population doubles every hour, it is GP.

3-mark answer

Many word problems become easier when we first decide whether the change is by repeated addition or repeated multiplication. Fixed salary increase usually forms an AP. Repeated doubling, percentage growth, or halving often forms a GP. AP model: an = a + (n - 1)d. GP model: an = a · r^(n - 1). Use AP for equal addition and GP for equal multiplication. A student saves Rs 200 in January and increases savings by Rs 50 each month. The sixth month saving is a6 = 200 + 5(50) = Rs 450, so the model is AP. Exam questions may describe salaries, savings, seating rows, tile patterns, population growth, or repeated discount and ask for a term or total. For fixed monthly increase, some students multiply by the increase and make it GP, but equal addition means AP.
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