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

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $\frac { 3 } { 2 } , \frac { 3 } { 8 } , \frac { 3 } { 32 } , \frac { 3 } { 128 } , \ldots$

Find the sum of all the integers from 65 to 95.

License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed?

Provide an appropriate response. -In your own words, explain how to determine the binomial coefficient for x $x ^ { 6 } y ^ { 4 } \text { in the expansion of } ( x + y ) ^ { 10 }$

A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many ways can you get 5 apples?

Find the nth term of the geometric sequence. - $a _ { 1 } = 1792 , r = \frac { 1 } { 4 } , n = 4$

Write the indicated term of the binomial expansion. - $( 3 x + 4 ) ^ { 5 } ; \quad 5$ th term

A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many ways can you get 5 oranges?

Write an equation for the ellipse. - $e = \frac { 7 } { 25 } ;$ vertices at $( 0 , - 25 ) , ( 0,25 )$

Find the nth term of the geometric sequence. -2 , 6 , 18 , . . . ; n = 7

Provide an appropriate response. -Convert the decimal .959595... to a fraction by writing it as the infinite series $\frac { 95 } { 100 } + \frac { 95 } { 100 ^ { 2 } } + \frac { 95 } { 100 ^ { 3 } } + \ldots$

Graph the parabola. - $x=(y-2)^{2}$

If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.04, what are the odds against a direct hit?

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

Write an equation for the ellipse. -foci at $( \pm 9,0 ) ; x$ -intercepts $( \pm 15,0 )$

Write the indicated term of the binomial expansion. - $( x + 2 y ) ^ { 12 ; } 4$ th term

Use a graphing calculator to evaluate the series. - $\sum _ { \mathrm { k } = 2 } ^ { 7 } \left( \mathrm { k } ^ { 2 } - 4 \mathrm { k } + 7 \right)$

A building has an entry the shape of a parabolic arch 46 ft high and 36 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Evaluate the expression. -C(11, 7)

Write an equation for the parabola. -vertex: $( 5 , - 3 )$ , directrix: $x = 13$