Exam 14: Sequences, Series, and the Binomial Theorem

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first eight terms of the arithmetic sequence $- 6 , - 16 , - 26 , \ldots$

Evaluate the expression. - $\frac { 7 ! } { 3 ! 4 ! }$

Evaluate the expression. - $\sum _ { i = 2 } ^ { 5 } ( 4 i - 3 )$

Solve the problem. -A pendulum swings through an arc 40 inches long on its first swing. Each swing thereafter, it swings only 60% as far as on the previous swing. How far will it swing altogether before coming to A complete stop? If necessary, round to the nearest inch.

Fill in the blank with one of the words or phrases listed below. general term common difference finite sequence common ratio Pascal's triangle infinite sequence factorial of series geometric sequence arithmetic sequence -A(n)--------- is a sequence in which each term (after the first) differs from the preceeding term by a constant amount d. The constant d is called the ----------of the sequence

Find the first five terms of the sequence. Round each term to four decimal places as necessary. - $a _ { n } = \left( 1 + \frac { 2 } { 3 n } \right) ^ { n } \quad$ Round each term to four decimal places when necessary.

Expand the binomial. - $( 5 x - 2 y ) ^ { 3 }$

Find the sum of the terms of the infinite geometric sequence. - $96,24,6 , \cdots$

Use the partial sum formula to find the partial sum of the given geometric sequence. -Find the sum of the first five terms of the geometric sequence $1,2,4 , \ldots$

Write the first five terms of the sequence whose general term is given. - $a _ { n } = n ^ { 2 } - n$

Solve the problem. -If $a _ { 1 }$ is $\frac { 1 } { 2 }$ , and $r$ is $- 2$ , find $\mathrm { S } _ { 10 }$ .

Evaluate the expression. - $\frac { 10 ! } { 5 ! 5 ! }$

Find the partial sum. -Find the sum of the first ten terms of the sequence whose general term is $a _ { n } = ( - 1 ) ^ { n }$ .

Evaluate the expression. - $\frac { 6 ! } { 0 ! }$

Fill in the blank with one of the words or phrases listed below. general term common difference finite sequence common ratio Pascal's triangle infinite sequence factorial of series geometric sequence arithmetic sequence -A(n) ----------is a sequence in which each term (after the first) is obtained by multiplying the preceeding term by a constant amount r. The constant r is called the of the sequence

Solve the problem. -Write $0.30 \overline { 30 }$ as an infinite geometric series and use the formula for $\mathrm { S } _ { \infty }$ to write it as a rational number.

Find the indicated term. -The ninth term of the expansion of $( 4 x + y ) ^ { 8 }$

Solve the problem. -If a $a _ { 1 }$ is $4 , a _ { 32 }$ is $\frac { 5 } { 3 }$ , and $d$ is $- \frac { 7 } { 93 }$ , find $S _ { 32 }$ .

Solve the problem. -The distance, in feet, that a car travels down the side of a mountain in each consecutive second is modeled by a sequence whose general term is $a _ { n } = 35 n - 17$ , where $n$ is the number of seconds. Find the distance the car travels in the fifth second.

Given are the first three terms of a sequence that is geometric. Find a1 and r. - $2,8,32$