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: 30 feet; rebounds $40 \%$

Find the first four terms of the given sequence. - $a_{1}=3, a_{n}=\left(a_{n}-1\right)^{2}$

Find the indicated partial sum for the given sequence -s6, 729, 2187, 6561, 19,683, ..

Find the indicated term. -Which term of the arithmetic sequence $4,10,16, \ldots$ , is equal to 154 ?

Find the indicated partial sum for the given geometric sequence - $s_{6}, 2,-2,2,-2, \ldots$

Evaluate the given binomial coefficient - ${}_4 \mathrm{C}_{1}$

Examine the differences for the sequence, and determine the type of expression - $2,2,8,18,32$

Find the general term, $a_n$ , of the given geometric sequence - $1, \frac{1}{7}, \frac{1}{49}, \ldots$

Find the indicated partial sum for the given sequence -Find the sum of the first 280 positive integers.

Find the common ratio, r, for the geometric sequence - $\frac{2}{3}, \frac{8}{3}, \frac{32}{3}, \frac{128}{3}, \frac{512}{3}, \ldots$

Find the indicated partial sum for the given sequence -s10, $92,3,-86,-175, \ldots$

Find the indicated partial sum for the given sequence - $\mathrm{s} 5,1,-1,1,-1, \ldots$

Find the partial sum of the arithmetic sequence with the given first term and common difference - $\mathrm{s}_{6}, \mathrm{a} 1=-12, \mathrm{~d}=-2$

Find the general term, $a_n$ , of the given geometric sequence - $8,4,2, \ldots$

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

Find the indicated partial sum for the given sequence -s10, 86, 84, 82, 80, ..

Find the indicated partial sum for the given sequence -Find the sum of the first 671 even positive integers.

Simplify. - $7 !+4 !$

Find the general term, $a_n$ , of the given geometric sequence - $1,8,64, \ldots$

Find the sum - $\sum_{\mathrm{i}=3}^{6} \frac{\left(\mathrm{i}^{2}-3\right)}{2}$