Exam 11: Further Topics in Algebra

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). -The first term is 22 , and the common difference is $7 ; \mathrm { n } = 5$

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 1 } = - 12 , d = 4 ; \quad n = 5$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). -The first term is $- 1 + \sqrt { 17 }$ , and the common difference is $4 ; \mathrm { n } = 3$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 4 } ( - 1 ) ^ { \mathrm { k } } ( \mathrm { k } + 5 )$

Use a graphing calculator to evaluate the series. - $\sum _ { j = 3 } ^ { 10 } \left( 5 j ^ { 2 } - 18 \right)$

It can be shown that $( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } \ldots$ is true for any real number n (not just positive integer values) and any real number x, where $| x | < 1$ Use this series to approximate the given number to the nearest thousandth. - $1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$

Evaluate the series, if it converges. - $- 6 - 4 - \frac { 8 } { 3 } - \frac { 16 } { 9 } + \ldots$

Provide an appropriate response. -Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?

Write the binomial expansion of the expression. - $( 3 x + 1 ) ^ { 4 }$

Decide whether the given sequence is finite or infinite. --5, -4, -3, -2

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 2 } = - 25 , a _ { 5 } = 35 ; \quad \mathrm { n } = 10$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 2 } ^ { 5 } 2 ^ { \mathrm { k } }$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots$

Solve the problem. -A musician plans to perform 9 selections. In how many ways can she arrange the musical selections?

Decide whether the given sequence is finite or infinite. - $\mathrm { a } _ { 1 } = 5 \text {; for } \mathrm { n } \geq 2 , \mathrm { a } _ { \mathrm { n } } = 4 \cdot \mathrm { a } _ { \mathrm { n } - 1 } + 8$

Evaluate the series, if it converges. - $\sum _ { \mathrm { k } = 1 } ^ { \infty } \left( \frac { 3 } { 10 } \right) ^ { \mathrm { k } }$

Find the probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

Solve the problem. -An ordinary die is tossed. What are the odds in favor of the die showing an odd number?

Find the sum of the first n terms of the following arithmetic sequence. - $- 5 , - 2,1 , \ldots ; \mathrm { n } = 10$

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth. - $\sum _ { i = 2 } ^ { 9 } - 2 ( 0.93 ) i$