NCERT Solutions Class 9 Maths Chapter 8 — Predicting What Comes Next: Exploring Sequences and Progressions#

Chapter 8 explores sequences and progressions — ordered lists of numbers that follow a rule. You will identify patterns, work with arithmetic progressions, and find the $n^{\text{th}}$ term so that you can predict any value in a sequence without listing every one before it.

Exercises#

• Exercise Set 8.1 — Explicit and recursive rules, checking whether a number is a term (6 questions)
• Exercise Set 8.2 — Arithmetic progressions: $n^{th}$ term, sums, word problems (7 questions)
• Exercise Set 8.3 — Geometric progressions, a bouncing ball, the Sierpiński carpet (7 questions)
• End-of-Chapter Exercises — AP and GP problems, consecutive sums, special recursive sequences (15 questions)

What you will learn#

• Sequences given by an explicit rule and by a recursive rule.
• Arithmetic progressions: the nth term, finding which term a number is, and sums.
• Geometric progressions: the nth term and real examples such as a bouncing ball.
• Special patterns like the Sierpiński carpet.

Key formulas and results#

• AP: $a_n = a + (n - 1)d$, and $S_n = \dfrac{n}{2}[2a + (n - 1)d]$.
• GP: $a_n = ar^{n - 1}$.

Read and revise#

• NCERT Class 9 Maths Chapter 8 (PDF) — the Ganita Manjari Part I chapter itself.
• All Class 9 Maths chapters from Ganita Manjari Part I and Part II.

Frequently asked questions#