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

Evaluate the sum using the given information. - $x _ { 1 } = - 2 , x _ { 2 } = 3 , x _ { 3 } = - 1$ , and $x _ { 4 } = - 3$ $\sum _ { i = 1 } ^ { 4 } \left( - x _ { i } ^ { 2 } - 2 \right)$

Write out the first five terms of the sequence. - $a _ { n } = ( - 1 ) ^ { n - 1 } ( 7 n - 3 )$

An ellipse has eccentricity between 0 and 1.

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $y ^ { 2 } = 36 - x ^ { 2 }$

The series $\ln ( x ) = ( x - 1 ) - \frac { ( x - 1 ) ^ { 2 } } { 2 } + \frac { ( x - 1 ) ^ { 3 } } { 3 } - \ldots + ( - 1 ) ^ { n - 1 } \frac { ( x - 1 ) ^ { n } } { n }$ can be used to estimate the value of ln(a) for any positive real number a such that $0 < \mathrm { a } \leq 2$ . Use the first five terms of this series to estimate $\ln ( 1.17 )$ . Round to the nearest thousandth.

What are the odds in favor of drawing a 4 from these cards?

Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = - 0.3 ( \mathrm { x } - 10 ) ^ { 2 } - 5$ is a parabola openingــــــــــ and is ــــــــــ than that of $y = x ^ { 2 }$ .

Give the focus, directrix, and axis for the parabola. - $- \frac { 1 } { 40 } x ^ { 2 } = y$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 24 , a _ { 5 } = 648$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $a _ { 3 } = - 17 , d = 9 , n = 5$

Graph the conic section. - $x^{2}-14 x-12 y+109=0$

Write an equation for the parabola with vertex at the origin. -Focus (0, 10)

Write the indicated term of the binomial expansion. - $( 5 x + 2 ) ^ { 3 }$ ; 3rd term

Evaluate the expression. -P(8, 8)

A projectile is thrown upward so that its distance above the ground after t seconds is h = -14t2 + 588t. After how many seconds does it reach its maximum height?

A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) all are from the same suit? b) all are hearts? c) exactly 2 are spades?

Write the indicated term of the binomial expansion. - $( 4 x - 2 y ) ^ { 11 ; } \quad 10$ th term

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $a _ { 1 } = 1 , d = 5 , n = 6$

List the elements in the sample space of the experiment. -A box contains 2 blue cards numbered 1 through 2, and 3 green cards numbered 1 through 3. List the sample space of picking a blue card followed by a green card.

Find the probability. -A bag contains 19 balls numbered 1 through 19. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?