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Question 15 - End-of-Chapter Exercises - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress
Last updated at June 9, 2026 by Teachoo
End-of-Chapter Exercises
Class 9
Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress
- Definition
- Explicit Rule for a Sequence
- Recursive Rule for a Sequence
- VirahΔnkaβFibonacci sequence
- Exercise Set 8.1
- Arithmetic Progressions
- Visualising an AP
- Sum of the First n Natural Numbers
- Exercise Set 8.2
- Geometric Progressions
- Fractals as a GP Sequence
- Visualising a GP
- Exercise Set 8.3
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End-of-Chapter Exercises
Transcript
Question 15 Suppose W_1=1,γ" " Wγ_2=2 and for π>2,γ" " Wγ_n=W_1+W_2+β―+W_(nβ2)+2. Find the values of W_1,γ" " Wγ_2,β¦,γ" " Wγ_8. Do you recognise this sequence? Finding the values of πΎ_π to πΎ_π Let's calculate carefully: π_1=π (Given) π_2=π (Given) π_3=π_1+2=1+2=π π_4=π_1+π_2+2=1+2+2=π π_5=π_1+π_2+π_3+2=1+2+3+2=π π_6=(1+2+3+5)+2=ππ π_7=(1+2+3+5+8)+2=ππ π_8=(1+2+3+5+8+13)+2=ππ The first 8 values are: 1,2,3,5,8,13,21,34 2. Do you recognize this sequence? Yes. This is the Fibonacci sequence. Even though the problem gave a complicated, drawn-out recursive rule involving adding 2 , the result is identical to the standard Fibonacci rule where every number is simply the sum of the two numbers right before it ( π_π=π_(πβ1)+π_(πβ2) ).
