Predicting What Comes Next : Exploring Sequences and Progressions — Important Questions
CBSE · Class 9 · Mathematics
99 important questions from Predicting What Comes Next : Exploring Sequences and Progressions for CBSE Class 9 Mathematics, with answers.
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Important Questions from Predicting What Comes Next : Exploring Sequences and Progressions
The sum of the first 24 natural numbers is subtracted from the sum of the first 58 natural numbers. What is 25 + 26 + ... + 58?
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1411
Use S_n = n(n+1)/2. S_58 = 58 × 59 / 2 = 1711. S_24 = 24 × 25 / 2 = 300. So 25 + 26 + ... + 58 = 1711 - 300 = 1411.
A ball starts from 24 feet and bounces to 3/4 of its previous height each time. After 7 bounces, what is the height in feet?
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About 3.20 feet
The height after each bounce forms a GP with first bounce 18 feet and ratio 3/4. After 7 bounces, height = 24 × (3/4)^7 = 3.2034375 feet, which is about 3.20 feet.
In the Sierpiński triangle, the number of black triangles at stage 5 is what value?
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243
The number of black triangles is t_n = 3^n. At stage 5, t_5 = 3^5 = 243.
In the Sierpiński triangle, what is the black area at stage 4 if stage 0 is taken as 1 square unit?
Show answer
81/256
The black area follows s_n = (3/4)^n. At stage 4, s_4 = (3/4)^4 = 81/256.
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- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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