Question 3 of 17intermediate💡 UnderstandShort Answer2 marks

Write an expression for the topmost row of a pyramid with 4 rows in terms of the values in the bottom row.

Correct Answer

Given: Bottom row values: a, b, c, d

Pattern: For a 3-row pyramid with bottom row a, b, c, the top is a + 2b + c.

Extension: For a 4-row pyramid, the coefficients follow the third row of Pascal's triangle: 1, 3, 3, 1.

Answer: Topmost row = a + 3b + 3c + d

Exercise: Figure it Out (Section 1) | Q: 2 | (Page Page 6)
For More Understanding

Explanation

The chapter shows that for a 3-row pyramid with bottom row a, b, c, the top is a + 2b + c. Extending this pattern, for a 4-row pyramid, the coefficients follow the third row of Pascal's triangle: 1, 3, 3, 1.

Solution Steps

  1. Identify the bottom row values: a, b, c, d

  2. Recognize the pattern from a 3-row pyramid: top = a + 2b + c

  3. Apply Pascal's triangle coefficients (1, 3, 3, 1) for a 4-row pyramid

  4. Write the expression: a + 3b + 3c + d

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