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Magazine Problem 1
Fill in each blank with the correct response. In each row of Pascal鈥檚 triangle, the first and last terms are _____, and each number in the interior of the triangle is the _____ of the two numbers just above it (one to the right and one to the left).
Problem 1
Write out \(S_{4}\) for each of the following, and determine whether it is true or false. $$S_{n}: 3+6+9+\cdots+3 n=\frac{3 n(n+1)}{2}$$
Problem 1
Write a sample space with equally likely outcomes for each experiment. Two ordinary coins are tossed.
Problem 1
In a geometric sequence, if any term after the first is divided by the term that precedes it, the result is the common _____ of the sequence.
Problem 1
In an arithmetic sequence, if any term is subtracted from the term that follows it, the result is the common _______________ of the sequence.
Problem 2
For the arithmetic sequence having \(a_{n}=2 n+4,\) the term \(a_{3}=\) ____________.
Problem 2
For the geometric sequence having \(a_{n}=(-2)^{n},\) the term \(a_{5}=\) _____.
Problem 2
Fill in each blank with the correct response. If there are 3 ways to choose a salad, 5 ways to choose an entr茅e, and 4 ways to choose a dessert, then there are _____ ways to form a meal consisting of these three choices.
Problem 2
Write out \(S_{4}\) for each of the following, and determine whether it is true or false. $$S_{n}: 1^{2}+2^{2}+3^{2}+\cdots+n^{2}=\frac{n(n+1)(2 n+1)}{6}$$
Problem 2
Write a sample space with equally likely outcomes for each experiment. Three ordinary coins are tossed.
