Question 8 of 19intermediate🔧 ApplyNumerical2 marks

By imagining a large version of your picture, or drawing it partially, as needed, can you see what will be the value of 1 + 2 + 3 + ... + 99 + 100 + 99 + ... + 3 + 2 + 1?

Correct Answer

Formula: 1 + 2 + 3 + ... + n + ... + 3 + 2 + 1 = n² Given: The sequence goes up to 100 and back down. Substitution: n = 100 Calculation: 100² = 10000 Answer: The value is 10000.

Exercise: Figure it Out (Section 4) | Q: 2 | (Page Page 8)
For More Understanding

Explanation

Following the pattern established in the chapter, adding counting numbers up and down gives square numbers. The sum 1+2+3+...+n+...+3+2+1 always equals n². In this case, the sequence goes up to 100 and back down, so n=100. Therefore, the sum equals 100²=10000. This can be visualized as a 100×100100 \times 100 square grid of dots.

Solution Steps

  1. Step 1: Recognize the pattern: 1+2+...+n+...+2+1 = n²

  2. Step 2: Identify that the sequence goes up to 100 and back down

  3. Step 3: Apply the formula: n = 100

  4. Step 4: Calculate: 100² = 10000

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