medium difficulty5 min

Word problems based on AP

Word problems based on AP are real-life questions where quantities change by a fixed amount and can be solved using AP formulas.

In one line: Story first, formula second.

Practice This Concept

Understand it

This topic connects AP with daily life situations such as savings, seats in rows, pages in books, salary patterns, and repeated measurements. The main task is to translate the story into a first term, a common difference, and a required term number or sum. Good exam answers show the conversion from words to formula clearly.

Example

A person saves 20 rupees in the first week and increases the saving by 5 rupees each week. This forms an AP.

Formula and rule

Use a_n = a + (n - 1)d for one term and S_n = n/2 [2a + (n - 1)d] for totals.

See it worked out

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

Worked example

1A student deposits 50 rupees in the first month and increases the deposit by 20 rupees each month.
2The 4th month deposit is 50 + 3(20) = 110 rupees.

Method you can reuse

1Read the story and identify the pattern.
2Write the first term and common difference.
3Decide whether the question asks for one term or a total.
4Apply the correct formula.

Visual tip

A small table of week number, amount, and increase often makes word problems easier to read.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the first step in solving an AP word problem?

Think first, then show answer

The first step is to identify the first term, the fixed change, and what the question is asking for. Then you can choose the correct AP formula.

Common wrong answer

A common wrong answer is to treat every word problem like a sum problem, even when only one term is needed.

Don't mix this up

Students often jump to formulas without identifying what the first term, common difference, and required quantity actually are.

Exam tip

Underline the changing quantity, the fixed increase, and the number asked in the question.

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

CBSE often frames AP as savings, arrangements, seating, or count-based problems that need translation into formula form.

1
Enough for 1 mark
Word problems based on AP are real-life questions where quantities change by a fixed amount and can be solved using AP formulas.
2
Add for 2 marks
Example: A person saves 20 rupees in the first week and increases the saving by 5 rupees each week. This forms an AP.
3
Add for 3 marks
This topic connects AP with daily life situations such as savings, seats in rows, pages in books, salary patterns, and repeated measurements.

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