Question 9 of 19intermediate🔧 ApplyShort Answer2 marks

Which sequence do you get when you start to add the All 1's sequence up? What sequence do you get when you add the All 1's sequence up and down?

Correct Answer

(a) Adding the All 1's sequence up: All 1's sequence: 1, 1, 1, 1, 1, ... Cumulative sums: 1, 1+1=2, 1+1+1=3, 1+1+1+1=4, ... ∴ Result: Counting numbers sequence: 1, 2, 3, 4, 5, ...

(b) Adding the All 1's sequence up and down: Pattern: 1, 1+1+1=3, 1+1+1+1+1=5, ... ∴ Result: Odd numbers sequence: 1, 3, 5, 7, 9, ...

Exercise: Figure it Out (Section 4) | Q: 3 | (Page Page 8)
For More Understanding

Explanation

The All 1's sequence is 1, 1, 1, 1, 1, ... Adding up means cumulative sums: 1, 1+1=2, 1+1+1=3, 1+1+1+1=4, ... giving counting numbers. Adding up and down means: 1 (just 1), 1+1+1=3 (up to second 1 and back), 1+1+1+1+1=5 (up to third 1 and back), giving odd numbers 1, 3, 5, 7, ...

Solution Steps

  1. The All 1's sequence is: 1, 1, 1, 1, 1, ...

  2. Adding up means cumulative sums: 1, 1+1=2, 1+1+1=3, 1+1+1+1=4, ...

  3. This gives the Counting numbers sequence: 1, 2, 3, 4, 5, ...

  4. Adding up and down means: 1, 1+1+1=3, 1+1+1+1+1=5, ...

  5. This gives the Odd numbers sequence: 1, 3, 5, 7, 9, ...

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