91Ó°ÊÓ

Find the indicated \(n\)th partial sum of the arithmetic sequence. $$a_{1}=15, a_{100}=307, \quad n=100$$

Find the sum of the finite geometric sequence. $$\sum_{i=1}^{7} 64\left(-\frac{1}{2}\right)^{i-1}$$

Write the first five terms of the sequence. (Assume that \(n\) begins with 0.) $$a_{n}=\frac{5}{n !}$$

Decide whether the sequence can be represented perfectly by a linear or a quadratic model. If so, then find the model. $$-2,1,6,13,22,33, \dots$$

In how many different ways can a jury of 12 people be randomly selected from a group of 40 people?

Find the partial sum. $$\sum_{n=1}^{50} n$$

A fire company keeps two rescue vehicles. Because of the demand on the vehicles and the chance of mechanical failure, the probability that a specific vehicle is available when needed is \(90 \% .\) The availability of one vehicle is independent of the availability of the other. Find the probability that (a) both vehicles are available at a given time, (b) neither vehicle is available at a given time, and (c) at least one vehicle is available at a given time.

Decide whether the sequence can be represented perfectly by a linear or a quadratic model. If so, then find the model. $$-1,8,23,44,71,104, \ldots$$

A U.S. Senate Committee has 14 members. Assuming party affiliation is not a factor in selection, how many different committees are possible from the 100 U.S. senators?

Find the sum of the finite geometric sequence. $$\sum_{i=1}^{12} 16\left(\frac{1}{2}\right)^{i-1}$$