91Ó°ÊÓ

In an arithmetic sequence, if any term is subtracted from the term that follows it, the result is the common _______________ of the sequence.

Fill in each blank with the correct response. The value of 0! is _____.

Write the first five terms of each sequence. \(a_{n}=n+1\)

Evaluate each expression. $${ }_{5} P_{0}$$

Find the common difference \(d\). $$ 10,5,0,-5,-10, \ldots $$

Use mathematical induction to prove that each statement is true for every positive integer value of \(n.\) $$1^{2}+2^{2}+3^{2}+\cdots+n^{2}=\frac{n(n+1)(2 n+1)}{6}$$

Write the first five terms of each arithmetic sequence. $$ a_{1}=5, d=4 $$

Find the indicated term for each sequence. $$ a_{n}=-9 n+2 ; \quad a_{8} $$

Use the fundamental principle of counting or permutations to solve each problem. In how many ways can 7 of 10 mice be arranged in a row for a genetics experiment?

Use the binomial theorem to expand each binomial. $$ (a-b)^{5} $$