Precalculus Unit 7 Lessons
An initial investment of $1,500 was made in the first month. In the second month, $1,507 was invested, while in the third month, the investment increased to $1,514. The monthly investments then continued using this arithmetic progression. How much was the portfolio worth after 60 months?
$102,390
Sheena put $75 down on a new refrigerator. She paid the remaining balance in 18 monthly installments starting with $42.50 in the first month, and then increasing the payments by $10 each month. If the installment plan charged no interest, what is the total amount Sheena paid for the refrigerator at the end of the 18 months?
$2,370
Expand the binomial using Pascal's Triangle for the coefficients. Simplify. (x-4)4
(X-4)^4 = x^4 - 16x^3 + 96x^2 - 256x + 256
Expand the binomial using Pascal's Triangle for the coefficients. Simplify. (x+4)4
(x+4)^4 = x^4 + 16x^3 + 96X^2 +256X + 256
Expand the binomial using Pascal's Triangle for the coefficients. Simplify. (x+a)2
(x+a)^2 = x^2 + 2xa + a^2
Find the missing terms of the geometric sequence.
-3, -6, -12, -24, -48
Find the indicated term of the arithmetic sequence. [2,-5,-12,-19,-26,...] a13 = 13th term
-82
Find the first five terms of the sequence beginning with n=0. an=n2/n!
0,1,2,1 1/2, 2/3
Find the coefficient for the term. y5
1
Find the indicated term of the geometric sequence. [1,4,16,64,...] Find the 6th term
1,024
Find the first five terms of the sequence beginning with n=0. an=(n+1)!/n!
1,2,3,4,5
Find the sum of the finite series. [6+12+18+24+...+126]
1,386
Find the coefficient for the term. x3y2
10
Find the sum of the finite geometric series. [1+3+9+27+81]
121
Find the coefficient for the term. x2y4
15
Find the sum of the finite geometric series. [3+6+12+24+48+96]
189
Solve the factorial expression. 12!/3!⋅11!
2
Use a graphing calculator to find the indicated term of the sequence. [3,9,27,...] 7th term
2,187
Find the first five terms of the sequence beginning with n=0. an=(n+2)!
2,6,24,120,720
Find the missing term, use the formula an = a(n-2) + a(n-1). 10th term = 34, 8th term = 13 Find the 9th term.
21
Solve the factorial expression. 3!⋅10!/4!⋅8!
22.5
Given terms in the Fibonacci sequence, use the formula an = a(n-2) + a(n-1) Find the next term. Use a calculator if needed. 12th term = 89, 13th term = 144, 15th term = 377 Find the 14th term.
233
Find the sum of the finite arithmetic series. [1+4+7+10+...+40]
287
Find the coefficient for the term. x2y
3
Choose the correct numbers on the blanks in the Pascal's Triangle.
3 5 21
Find the value of the convergent series: [4+(-1)+1/4+(-1/16)+1/64+...]
3 1/5
∑4*0.5^n
3.875
Solve the factorial expression. 8!/5!
336
Given terms in the Fibonacci sequence, use the formula an = a(n-2) + a(n-1) Find the next term. Use a calculator if needed. 7th term = 8, 8th term = 13, 9th term = 21 Find the 10th term.
34
Find the indicated term of the arithmetic sequence. [5,8,11,14,17,...] a11 = 11th term
35
Use a graphing calculator to find the value of the factorial. 9!
362,880
Find the sum of the finite arithmetic series.[-2+4+10+16+...+64]
372
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 value of the convergent series: [2+1+12+14+18+...]
4
∑(1/2n+6)
46 1/2
Use a graphing calculator to find the value of the factorial. 12!
479,001,600
∑16*(3/4)^n
48
Use a graphing calculator to find the value of the factorial. 13!
6,227,020,800
Find the indicated term of the arithmetic sequence. [-11,-8,-5,-2,1,...] a25 = 25th term
61
Find the number of trailing zeros. Use a calculator to help with division. 2,523!
628
Find the sum of the finite series. [-7+(-4)+(-1)+2+...+62]
660
Riley was determined to be on the basketball team. He started practicing for 40 minutes on the first day, and then increased his practice time by 20 minutes on each subsequent day. With that pattern, how many total minutes will he have practiced in 25 days?
7,000 minutes
Find the indicated term of the geometric sequence. [2,8,32,128,...] Find the 7th term
8,192
Find the sum of the finite geometric series. [(-4)+12+(-36)+108]
80
Find the indicated term of the arithmetic sequence. [-7,-2,3,8,13,...] a20 = 20th term
88
Find the sum of the finite series. [5+10+15+20+...+95]
950
Use a graphing calculator to find the indicated term of the sequence. [6,12,24,...] 5th term
96
Given terms in the Fibonacci sequence, use the formula an = a(n-2) + a(n-1) Find the next term. Use a calculator if needed. Previous two terms are 377 and 610, Find the 17th term.
987
Find the specific formula for the sequence. [5,3,-2,7,1,...]
Cannot be done since the difference "d" is not constant through the sequence.
_____ are the result of positive consecutive numbers being multiplied together.
Factorials
Decide on Yes if the sequence is part of the Fibonacci sequence or No if it is not. {1,2,3,7,8}
NO
_____ means follow one after another.
Order
Use the table to help find a formula for the sequence. Write the formula in the parentheses next to the word Rule and complete the Rule column.
Term(Value) - Rule a.(a.) 1 - h 4 - b 7 - i 10 - c 13 -g
Use the table to help find a formula for the sequence. Write the formula in the parentheses next to the word Rule and complete the Rule column.
Term(Value) - Rule a.(c.) 0 - d 3 - h 8 - f 15 - e 24 -g
Use the table to help find a formula for the sequence. Write the formula in the parentheses next to the word Rule and complete the Rule column.
Term(Value) - Rule a.(c.) 6 - h 7 - i 8 - f 9 - a 10 -e
Decide on Yes if the sequence is part of the Fibonacci sequence or No if it is not. {3,5,8,13,21}
YES
Decide on Yes if the sequence is part of the Fibonacci sequence or No if it is not. {8,13,21,34}
YES
Define limit:
a boundary beyond which you cannot go
Find the first five terms of the sequence: an = 2n-4
a1 = a a2 = c a3 = g a4 = k a5 = h Write the terms in sequence H
Find the first five terms of the sequence: an =(-2)n
a1 = b a2 = k a3 = h a4 = f a5 = c Write the terms in sequence E
Find the first three terms of the sequence: an = 9/n
a1 = c a2 = e a3 = b
Find the first five terms of the sequence: an = n^2-3
a1 = e a2 = a a3 = b a4 = i a5 = j Write the terms in sequence K
Find the first three terms of the sequence: an = 3n^2-5
a1 = f a2 = d a3 = e
Find the first five terms of the sequence: an =n/n+1
a1 = j a2 = h a3 = i a4 = k a5 = e Write the terms in sequence B
Find the specific formula for the sequence. [12,1,112,2,212,...]
an=1/2n
Find the specific formula for the sequence. [3,7,11,15,19,...]
an=4n-1
Find the specific formula for the sequence. [-6,-1,4,9,14,...]
an=5n-11
Define convergent:
approaching a limit
Find the partial terms that are missing. Use the binomial theorem to find each coefficient. (x+y)8
b. d.
Decide whether the sequence is convergent or divergent: [1,12,14,18,116,...]
convergent
Decide whether the sequence is convergent or divergent: [5,2.5,1.25,0.625,0.3125,...]
convergent
Use the ratio test. Determine whether it converges or diverges. [3+1.5+0.75+0.375+...]
converges
Use the ratio test. Determine whether it converges or diverges. [4+1+1/4+1/16+1/64+...]
converges
Find the partial terms that are missing. Use the binomial theorem to find each coefficient. (x+y)7
d. a.
Decide whether the sequence is convergent or divergent: [4,6,8,10,12,...]
divergent
Use the ratio test. Determine whether it converges or diverges. [3+12+48+192+768+...]
diverges
Define infinite:
having an unlimited amount or number
The symbol for n factorial is _____.
n!
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 Fibonacci sequence is a _____ sequence.
recursive
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
In a Fibonacci sequence, you add the previous _____ numbers to get the next one.
two
Expand the binomial using Pascal's Triangle for the coefficients. Simplify. (x-3)3
x-3^3 = x^3 - 9x^2 + 27x -27