Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Use the summation properties to evaluate the series. The following rules may be needed: $\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$ - $\sum _ { i = 1 } ^ { 4 } \left( 4 i ^ { 2 } + 3 i - 1 \right)$

Find the future value of the annuity. -To save for retirement, you decide to deposit $2500 into an IRA at the end of each year for the next 35 years. If the interest rate is 1% per year compounded annually, find the value of the IRA, rounded to the nearest dollar, After 35 years.

A fair spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on an even number or a multiple of 3?

Choose the equation that matches the graph. -

Match the equation of the parabola with the appropriate description. - $x = 2 y ^ { 2 } - 3 y + 4$

Bruce agrees to go to work for Jim at a rate of 3¢ for the first day, 6¢ for the second day, 12¢ for the third day, 24¢ for the fourth day, and so on. What will Bruce's daily pay be on day 10, and how much total wages will he Have earned at the end of that day?

Find all natural number values for n for which the given statement is false. - $2 ^ { n } > 2 n + 2$

Decide whether the given sequence is finite or infinite. - $\mathrm { a } _ { 1 } = 3 , \mathrm { a } _ { 2 } = 8 ; \text { for } 3 \leq \mathrm { n } \leq 10 , \mathrm { a } _ { \mathrm { n } } = 4 \cdot \mathrm { a } _ { \mathrm { n } - 1 } + 7 \cdot \mathrm { a } _ { \mathrm { n } - 2 }$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } = 16 y ^ { 2 } + 64$

Identify the type of graph. - $10 x ^ { 2 } + 100 x + 10 y ^ { 2 } - 220 y = - 1459$

A die is rolled 11 times. Find the probability of rolling exactly 11 ones.

Identify the type of graph. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 9 } = 1$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \frac { 2 n } { n + 9 }$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $a _ { 1 } = 8.622 , r = 3.579$ (Round to the nearest hundredth)

How many ways can a committee of 4 be selected from a club with 12 members?

Give the focus, directrix, and axis for the parabola. - $( y - 8 ) ^ { 2 } = - 12 ( x + 4 )$

Write an equation for the ellipse. -foci at $( 0,11 ) , ( 0 , - 11 )$ , through the point $\left( 1 , \frac { 61 \sqrt { 3599 } } { 60 } \right)$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x + 1 = ( y + 8 ) ^ { 2 }$

Find a general term a_n for the geometric sequence. - $a _ { 1 } = \frac { 1 } { 6 } , r = - 3$

Evaluate the expression. -C(4, 0)