Class 9 Mathematics Chapter 8 Predicting What Comes Next?: Exploring Sequences and Progressions – Revision Notes

Sequences follow a rule from one term to the next, and this chapter zooms in on arithmetic progressions, where a constant common difference lets you find any term or sum using two key formulas.

Last Updated: September 23, 2026

Sequences

• Ordered list of numbers following a rule; each number = a term.

Arithmetic Progression (AP)

• Constant common difference (d) between consecutive terms.
• Form: a, a+d, a+2d, …

Key Formulas

• nth term: a_n = a + (n−1)d.
• Sum of n terms: S_n = n/2 × [2a + (n−1)d] = n/2 × (a + a_n).

Identifying an AP

• Check: difference between every pair of consecutive terms is the same.

One-Line Summary

An arithmetic progression is a sequence with a constant common difference, and its nth term and sum of n terms can be found directly using two key formulas, useful for modelling steady real-world change.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

What is the difference between an arithmetic progression and a general sequence?
A general sequence is simply an ordered list of numbers following any pattern or rule, while an arithmetic progression is a specific type of sequence where the difference between consecutive terms remains constant throughout.

How is the sum of the first n terms of an arithmetic progression calculated?
The sum of the first n terms of an arithmetic progression is calculated using a formula based on the number of terms, the first term, and the common difference, avoiding the need to add every term individually.

Written by Satish

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