Exam 9: Sequences Series and Probability

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$

If the statement P₁ is true but the true statement P₆ does not imply that the statement P₇ is true, then P_n is not Necessarily true for all positive integers n.

Evaluate the sum. $\sum _ { k = 1 } ^ { 6 } 5 k$

A deposit of $ 5000 is made in an account that earns 8 % interest compounded monthly.The balance in the account after n months is given by $A _ { n } = 5000 \left( 1 + \frac { 0.08 } { 12 } \right) ^ { n } , n = 1,2,3 , \ldots$ Find the balance in the account after 8 years by finding the 96th term of the sequence.Round to the nearest penny.

Use the Binomial Theorem to expand and simplify the expression. $( y - 3 ) ^ { 5 }$

The probability that a basketball player will make a given free throw is $\frac { 6 } { 10 }$ .To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term ${ } _ { 10 } C _ { 8 } \left( \frac { 6 } { 10 } \right) ^ { 8 } \left( \frac { 4 } { 10 } \right) ^ { 2 }$ in the expansion of $\left( \frac { 6 } { 10 } + \frac { 4 } { 10 } \right) ^ { 10 }$ .Round to four decimal places.

Find the first five terms of the geometric sequence. $a _ { 1 } = 5 , r = 3$

Find a formula for a_n for the arithmetic sequence. A₁ = -5, a₅ = 18

There were approximately 42 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is 45 or older? ( $a = 42 \%$ and $b = 39 \%$ )

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms a

Evaluate ${ } _ { n } P _ { r }$ . $100 P _ { 3 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 x - 5 y ) ^ { 5 }$

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x.) $( 5 x - 2 y ) ^ { 6 } , n = 3$

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 7 } P _ { 3 }$

Write the nth term of the arithmetic sequence as a function of n. ​ A₁ = -7, ak _{+ 1} = a_k + 4

A principal of $4000 is invested at 8% interest.Find the amount after 10 years if the interest is compounded quarterly. ​

Find the number of diagonals of a dodecagon (12 sides).(A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

In how many ways can seven children posing for a photograph line up in a row? ​

Find the sum. $\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )$