medium difficulty5 min

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.

In one line: Same add means AP; same multiply means GP.

Practice This Concept

Understand it

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.

Example

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

Formula and rule

AP model: an = a + (n - 1)d.

GP model: an = a · r^(n - 1).

Use AP for equal addition and GP for equal multiplication.

See it worked out

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

Worked example

1A student saves Rs 200 in January and increases savings by Rs 50 each month.
2The sixth month saving is a6 = 200 + 5(50) = Rs 450, so the model is AP.

Method you can reuse

1Read the story carefully.
2Identify the first value.
3Decide if the change is fixed addition or fixed multiplication.
4Choose AP or GP.
5Substitute into the correct formula.
6Interpret the answer with units.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

Common wrong answer

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

Don't mix this up

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

Exam tip

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