Question 3 of 25intermediate🔧 ApplyNumerical3 marks

If there are multiple strikes causing movements in the order 1, −2, 3, −4, ..., −10, what is the final position of the coin?

Correct Answer

Given: The movements are in the order 1, −2, 3, −4, ..., −10

Formula: Final position = Sum of all movements

Solution: Step 1: Identify the sequence of movements: 1, −2, 3, −4, 5, −6, 7, −8, 9, −10 Step 2: Group the terms: (1 + (−2)) + (3 + (−4)) + (5 + (−6)) + (7 + (−8)) + (9 + (−10)) Step 3: Calculate each pair: −1 + (−1) + (−1) + (−1) + (−1) Step 4: Sum all: −1×51 \times 5 = −5

Answer: The final position of the coin is −5.

Exercise: Carrom Coin Integers | Q: 2 | (Page Page 4)
For More Understanding

Explanation

The chapter explains that when there are multiple strikes, the final position is the sum of all movements. The movements are in the order 1, −2, 3, −4, ..., −10. This is an alternating sequence from 1 to 10 with alternating signs. We need to find: 1 + (−2) + 3 + (−4) + 5 + (−6) + 7 + (−8) + 9 + (−10).

Solution Steps

  1. Step 1: Identify the sequence of movements: 1, −2, 3, −4, 5, −6, 7, −8, 9, −10

  2. Step 2: Group the terms: (1 + (−2)) + (3 + (−4)) + (5 + (−6)) + (7 + (−8)) + (9 + (−10))

  3. Step 3: Calculate each pair: −1 + (−1) + (−1) + (−1) + (−1)

  4. Step 4: Sum all: −1×51 \times 5 = −5

  5. Step 5: The final position is −5

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