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
