Exam 14: Sequences, Series, and the Binomial Theorem

Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1 and d. If a sequence is geometric, find a1 and r. - $2,6,18 , \ldots$

Solve the problem. -Doctors predict that by administering a vaccine, the number of new cases of a certain childhood disease will decrease by half each year. If 1000 people were afflicted with the disease in 2010,Estimate the number of new cases in 2015. (Round to the nearest whole number, if necessary.)

Use Pascal's triangle to expand the binomial. - $( p + q ) ^ { 5 }$

Solve the problem. -Find the sum of the first 50 positive odd integers.

Find the indicated term of the sequence. -The twenty-fifth term of the arithmetic sequence $6 \sqrt { 3 } , 2 \sqrt { 3 } , - 2 \sqrt { 3 } , \ldots$

Provide an appropriate response. -Expand the expression $\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }$ .

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given. - $\mathrm { a } _ { 1 } = - 20 ; \mathrm { d } = 4$

Solve the problem. -Ms. Patterson proposes to give her daughter Claire an allowance of $\$ 0.05$ on the first day of her 13-day vacation, $\$ 0.10$ on the second day, $\$ 0.20$ on the third day, and so on. Write an equation of a sequence whose terms correspond to Claire's potential allowance. Find the allowance Claire would receive on the last day of her vacation.

Find the indicated term of the sequence. -The fifth term of the arithmetic sequence whose first term is $- 4$ and whose common difference is $- 3$

Solve the problem. -Find the sum of the first 30 terms of the arithmetic sequence -7, 2, 11, 20, . . .

Solve the problem. -Find the sum of the first eleven terms of the sequence $- 9 , - 1,7,15 , \ldots , 71$ where 71 is the eleventh term.

Solve the problem. -While bungee jumping, Gregory falls from a height of 80 feet. He continues to bounce one-half the height from which he last fell. Write out the first five terms of this geometric sequence and find the general term.

Use the binomial formula to expand the binomial. - $( 5 x + 4 ) ^ { 3 }$

Find the indicated term for the sequence whose general term is given. - $a _ { n } = 4 ( 2 n - 2 ) ; a _ { 14 }$

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 4, -8, 16, . . .

Find the indicated term for the sequence whose general term is given. - $a _ { n } = \frac { 1 } { n ^ { 2 } } ; a _ { 5 }$

Find the partial sum. -Find the sum of the first three terms of the sequence whose general term is given by $a _ { n } = ( n - 9 ) ^ { 2 }$ .

Solve the problem. -If $\mathrm { a } _ { 1 }$ is 1 , and $\mathrm { r }$ is $\frac { 1 } { 4 }$ , find $\mathrm { S } _ { 5 }$ .

Solve the problem. -A brick staircase has a total of 18 steps. The bottom step requires 113 bricks. Each successive step requires 4 less bricks than the prior one. How many bricks are required to build the staircase?

Solve the problem. -A new exhibit is scheduled to open at the local museum. Museum officials expect that 9000 people will visit the exhibit in its first week, and that the number of visitors will drop by 40 people per week after the first week during the first 6 months. Write out the first five terms of the sequence, and find the total number of visitors expected in the exhibit's first 7 weeks.