Question

question 5 of 10 which of the following statements regarding pascals triangle are correct? a. to generate pascals triangle, add adjacent terms on a row to determine the term directly below them. b. each row is a \palindrome\ - that is, it is the same if read from left to right or from right to left. c. the coefficients of (x + y)^n are given by the nth row of pascals triangle. d. the nth row gives the coefficients in the expansion of (x + y)^(n - 1).

Explanation:

• A: This is the rule for constructing Pascal's triangle. Adding adjacent terms in a row gives the term below them.
• B: Pascal's triangle rows are symmetric, so they are palindromes.
• C: The coefficients of the binomial expansion \((x + y)^n\) are found in the \(n\)th row of Pascal's triangle.
• D: The \(n\)th row gives coefficients of \((x + y)^n\), not \((x + y)^{n - 1}\).

Answer:

A. To generate Pascal's triangle, add adjacent terms on a row to determine the term directly below them.
B. Each row is a "palindrome" - that is, it is the same if read from left to right or from right to left.
C. The coefficients of \((x + y)^n\) are given by the \(n\)th row of Pascal's triangle.