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Exam 14: Sequences, Series, and the Binomial Theorem

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Question 41

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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 $- 6 , - 16 , - 26 , \ldots$

A) $- 48$
B) $- 128$
C) 328
D) $- 328$

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Question 42

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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.

A) $\frac { 10 } { 33 }$
B) $\frac { 10 } { 333 }$
C) $\frac { 20 } { 33 }$
D) $\frac { 1 } { 3 }$

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Question 43

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

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

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

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.

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

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

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

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

Fill in the blank with one of the words or phrases listed below. $\begin{array} { l l l l } \text { general term } & \text { common difference } & \text { finite sequence } & \text { common ratio } \\\text { Pascal's triangle } & \text { infinite sequence } & \text { factorial of } \mathbf { n } & \text { series } \\\text { geometric sequence } & \text { arithmetic sequence } & &\end{array}$ -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 partial sum. -Find the sum of the first ten terms of the sequence whose general term is $a _ { n } = ( - 1 ) ^ { n }$ .

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

Fill in the blank with one of the words or phrases listed below. $\begin{array} { l l l l } \text { general term } & \text { common difference } & \text { finite sequence } & \text { common ratio } \\\text { Pascal's triangle } & \text { infinite sequence } & \text { factorial of } \mathbf { n } & \text { series } \\\text { geometric sequence } & \text { arithmetic sequence } & &\end{array}$ -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

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

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

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

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 $1,2,4 , \ldots$

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.

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.