Precalculus Unit 7 Quizzes

Expand the binomial using Pascal's Triangle for the coefficients. Simplify. (x+5)3

(x+5)^3 = x^3 + 15x^2 + 75x + 125

Expand the binomial using Pascal's Triangle for the coefficients. Simplify. (x-3)4

(x-3)^4 = x^4 - 12x^3 + 54x^2 - 108x + 81

Find the indicated term of the arithmetic sequence. [4,1,-2,-5,-8,...] 14th term

-35

Find the a5of the sequence. an=(n!)-3

117

Find the indicated term of the geometric sequence. [3,12,48,192,...] Find the 7th term a1=3, r= 12/3 =4

12,288

Find the indicated term of the geometric sequence. Find the 12th term a1=7, r=2

14,336

Solve the factorial expression. (5!)(7!)(3!)(6!)

140

Write the correct numbers on the blanks in the Pascal's Triangle. (top to bottom)

2 3 10 6 21

Find the sum of the finite geometric series. [2+6+18+54+162]

242

Find the number of trailing zeros. Use a calculator to help with division. 1,027!

255

Find the indicated term of the arithmetic sequence. [-12,0,12,1,112,...] 9th term

3 1/2

Find the a5of the sequence. an=n!/4

30

Find the sum of the finite series. [2+5+8+11+...+44]

345

Find the missing term, use the formula an = a(n-2) + a(n-1). 14th term = 233, 16th term = 610 Find the 15th term.

377

Find the indicated term of the arithmetic sequence. [3,7,11,15,19,...] 10th term

39

Find the sum of the finite series. [7+12+17+22+...+632]

40,257

Find the sum of the finite geometric series. [5+20+80+320]

425

Find the partial term that is missing. Use the binomial theorem to find the coefficient. (x-y)4=x4-4x3y+6x2y2- _____ +y4

4xy^3

Find the missing term, use the formula an = a(n-2) + a(n-1). 4th term = 2, 5th term = 3 Find the 6th term.

5

Solve the factorial expression. 10!/6!

5,040

Use a graphing calculator to find the value of the factorial. 7!

5,040

Find the sum of the finite series. [-3+0+3+6+...+54]

510

Find the a5of the sequence. an=(n-2)!

6

Solve the factorial expression. 6!/(2!)(3!)

60

Find the partial term that is missing. Use the binomial theorem to find the coefficient. (x+y)6=x6+ _____ +15x4y2+20x3y3+15x2y4+6xy5+y6

6x^5y

Use a graphing calculator to find the value of the factorial. 6!

720

Find the missing term, use the formula an = a(n-2) + a(n-1). 9th term = 21, 8th term = 13 Find the 7th term.

8

Find the sum of the finite geometric series. [(-4)+8+(-16)+32+(-64)+128]

84

Find the missing term, use the formula an = a(n-2) + a(n-1). 10th term = 34, 11th term = 55 Find the 12th term.

89

Define limit:

a boundary beyond which you cannot go

Find the first five terms of the sequence: an = n^3

a1 = 1 a2 = 8 a3 = 27 a4 = 64 a5 = 125

Find the first five terms of the sequence: an = (2n)2

a1 = 4 a2 = 16 a3 = 36 a4 = 64 a5 = 100

Find the first five terms of the sequence: an = 5n

a1 = 5 a2 = 10 a3 = 15 a4 = 20 a5 = 25

Find the first five terms of the sequence: an = n^2/2

a1 = g a2 = e a3 = a a4 = d a5 = f

Find the first five terms of the sequence: an = n/2

a1 = g a2 = e a3 = h a4 = f a5 = d

Find the specific formula for the sequence. [6,12,18,24,30,...]

an = 2n-1

Find the specific formula for the sequence. [1,4,7,10,13,...]

an = 3n-2

Find the specific formula for the sequence. [-2,4,10,16,22,...]

an = 6n-8

What is the formula for finding a term of a geometric sequence?

an = a1r ^n-1

Define convergent:

approaching a limit

Use the ratio test. Determine whether it converges or diverges. [3+1+13+19+127+...]

converges

Use the ratio test. Determine whether it converges or diverges. [4+1+14+116+164+...]

converges

Use the ratio test. Determine whether it converges or diverges. [1+7+49+343+...]

diverges

Define infinite:

having an unlimited amount or number

Define divergent:

not approaching a limit

The letter, n, stands for the _____ of a term in a sequence.

position

What is the formula for the ratio test of an infinite geometric series?

r = lim [ an+1/an ]

A _____ is an orderly collection of terms.

sequence

What is the formula for finding the value of a convergent infinite geometric series?

s∞ = a1/1-r