Chapter 8: Predicting What Comes Next: Exploring Sequences and ProgressionsClass 9 Mathematics — summary, notes, extra questions & NCERT solutions

Summary

This chapter studies sequences — ordered lists of numbers whose entries are called terms — and ways to describe them. Familiar examples include natural, odd, triangular and square numbers. A sequence can be given by an explicit rule, which computes the \(n\)th term directly from its position, such as \(t_n = 2n-1\) for the odd numbers; or by a recursive rule, which builds each term from earlier ones, such as the Virahanka-Fibonacci rule \(V_n = V_{n-1} + V_{n-2}\). An arithmetic progression (AP) has a constant common difference \(d\); its \(n\)th term is \(t_n = a + (n-1)d\), and its points lie on a straight line. A geometric progression (GP) has a constant common ratio \(r\); its \(n\)th term is \(t_n = ar^{n-1}\), and its points do not lie on a line. The sum of the first \(n\) natural numbers, first written by Aryabhata, is \(\dfrac{n(n+1)}{2}\), which is also the \(n\)th triangular number. Fractals such as the Sierpinski triangle and square carpet generate geometric progressions in both their counts and areas.

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Extra questions & answers

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Exercise Set 8.1

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Exercise Set 8.2

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Exercise Set 8.3

End-of-Chapter Exercises

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