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Chapter 5 · Question 1

What is an arithmetic progression? Find the common difference of 45,43,41,39,…45,43,41,39,\ldots.

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Q1

What is an arithmetic progression? Find the common difference of 45,43,41,39,…45,43,41,39,\ldots.

Answer Revealed
Direct Answer:
An arithmetic progression is a list of numbers in which the difference between consecutive terms is constant. For 45,43,41,39,…45,43,41,39,\ldots, common difference d=43−45=−2d=43-45=-2.

Simple Explanation

If the same number is added each time, it is an AP. Here −2-2 is added each time.

Exam-Ready Structure

A sequence a1,a2,a3,…a_1,a_2,a_3,\ldots is an AP if an+1−ana_{n+1}-a_n is constant. This constant is the common difference dd. Here 43−45=−243-45=-2, 41−43=−241-43=-2, and 39−41=−239-41=-2, so it is an AP with d=−2d=-2.

Key Points

  • An arithmetic progression is a list of numbers in which the difference between consecutive terms is constant.
  • Use the NCERT formula or theorem carefully.
  • Write units and final conclusion where applicable.

Related Questions

Q2

State the formula for the nnth term of an AP and use it to find the 20th term of 3,7,11,15,…3,7,11,15,\ldots.

Q3

How many terms are there in the AP 7,10,13,…,437,10,13,\ldots,43?

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