alleryStart learning →How is each interior entry of Pascal's Triangle produced?
ABy doubling the entry to its left
BBy adding the two entries just above
CBy multiplying the two above it
DBy subtracting the entry above it
Answer & Solution
Correct answer: B. By adding the two entries just above
1. Every row of Pascal's Triangle is flanked at both ends by 1.
2. Each entry between those ends is the sum of the two entries immediately above it.
3. So the row 1, 3, 3, 1 produces the next row as 1, 1 + 3, 3 + 3, 3 + 1, 1, which is 1, 4, 6, 4, 1.
4. Multiplying the pair above would give 3 and 9 rather than 4 and 6, so the operation really is addition.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.6 Binomial Theorem_
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