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Question 15 - End-of-Chapter Exercises - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress
Last updated at August 12, 2026 by Teachoo
End-of-Chapter Exercises
Maths Class 9
Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress
- Definition
- Explicit Rule for a Sequence
- Recursive Rule for a Sequence
- VirahฤnkaโFibonacci 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
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Transcript
Question 15 Suppose W_1=1,ใ" " Wใ_2=2 and for ๐>2,ใ" " Wใ_n=W_1+W_2+โฏ+W_(nโ2)+2. Find the values of W_1,ใ" " Wใ_2,โฆ,ใ" " Wใ_8. Do you recognise this sequence? Finding the values of ๐พ_๐ to ๐พ_๐ Let's calculate carefully: ๐_1=๐ (Given) ๐_2=๐ (Given) ๐_3=๐_1+2=1+2=๐ ๐_4=๐_1+๐_2+2=1+2+2=๐ ๐_5=๐_1+๐_2+๐_3+2=1+2+3+2=๐ ๐_6=(1+2+3+5)+2=๐๐ ๐_7=(1+2+3+5+8)+2=๐๐ ๐_8=(1+2+3+5+8+13)+2=๐๐ 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 ( ๐_๐=๐_(๐โ1)+๐_(๐โ2) ).
