Exam 11: Sequences, Series, and the Binomial Theorem

Find the total distance traveled by a ball, given its starting height and the percent of its height that it rebounds to after bouncing. Round to the nearest tenth of a foot if necessary. -Starting height: 8 feet; rebounds $70 \%$

Find the common ratio, r, for the geometric sequence - $1,-3,9,-27,81, \ldots$

Use the formulas $\sum_{i=1}^{n} i=\frac{n(n+1)}{2}, \sum_{i=1}^{n} i^{2}=\frac{n(n+1)(2 n+1)}{6}$ , and $\sum_{i=1}^{n} i^{3}=\left[\frac{n(n+1)}{2}\right]^{2}$ to find the sum. -Find the sum of the first 70 cubed positive integers.

Find the first five terms of the arithmetic sequence with the given first term and common difference - $\mathrm{a}_{1}=-17, \mathrm{~d}=4$

Find the indicated partial sum for the given sequence - $s_{6}, 5,7,9,11, \ldots$

Write the sum using summation notation - $18+30+42+54+66$

Find the first five terms of the sequence with the given general term. - $a_{n}=(-1)^{n+1}$

Find the indicated partial sum for the given sequence - $s_{6}, 3,-8,13,-18, \ldots$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $a_{n}=4 \cdot(1)^{n}$

Solve the problem. -Jackie is considering a job that offers a monthly starting salary of $\$ 2500$ and guarantees her a monthly raise of $\$ 140$ during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.

Find the indicated term. -Which term of the arithmetic sequence $11,6,1, \ldots$ , is equal to - 489 ?

Find the general term $a_n$ of the given sequence - $2,6,10,14,18, \ldots$

Simplify. - $\frac{7 !}{0 ! \cdot 7 !}$

Find the indicated partial sum for the given sequence -s8, $1,-5,9,-13, \ldots$

Find the indicated term for the sequence. -Find the $11^{\text {th }}$ term of the sequence whose general term is $a_{n}=n^{2}-n$ .

Solve the problem. -The number of students in a school in year $n$ is estimated by the model $a_{n}=6 n^{2}+13 n+83$ . Write a sequence showing how many students are in the school in each of the first three years.

Solve. -One approximation for Euler's number e is the infinite sum $1+\sum_{\mathrm{i}=1}^{\infty} \frac{1}{\mathrm{i} !}=1+$ $\left.\left(\frac{1}{1}+\frac{1}{1 \cdot 2}+\frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{1 \cdot 2 \cdot 3 \cdot 4}+\ldots\right).\right)$ The expression $\mathrm{i}$ ! is called $\mathrm{i}$ factorial and is equal to the product of the integers from 1 through $i$ . Find the sum through $i=9$ , rounded to the nearest thousandth.

Simplify. -8 !

Find the sum - $\sum_{i=1}^{4}\left(i^{2}-5 i-3\right)$

Find the general term, $a_n$ , of the given geometric sequence - $\frac{1}{6}, \frac{1}{2}, \frac{3}{2}, \ldots$