1 72 a. Find c and c a (6) a1 + (7)ªn-2 b= €₂ = r²c₁r = c ₂ = 0 b. Substitute c, and c, into the following equation: c. Identify a, b, and c in the quadratic equation. Show your work here: C= d. Use the quadratic formula to find the two roots. Here is the quadratic formul -b± √b² - 4ac 2a Show your work here: -b± √b² - 4ac 2a

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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13. Solve the recurrence relation. Given:
a0=3

a1= 6

an= 6a n-1 + 7a n-2

Show your work in the space provided.

a. Find c1 and c2 

an= (6)a n-1 + (7)a n-2

c1= 

c2= 

 

b. Substitute c1 and c2 into the following equation: 

r^2- c1r - c2= 0 

show your work here:

 

 

c. Identify a, b, and c in the quadratic equation.

a= 

b= 

c= 


d. Use the quadratic formula to find the two roots. Here is the quadratic formula:

-b + Vb^2- 4ac/2a

Show your work here:


e. Substitute two roots, r1 and r2 into the equation an= a1r1^n+ a2r2^n

Show your work here:

 

 

f. Now substitute to find two equations, a0 and a1 Remember to use the equation you found from step e.

show your work here:

a0= 3 =
a1= 6 =


g. Add the two equations together find a1 and a2 

a1= 

a2=

 

h. What is the solution to the recurrence relations?

an= 

 

i. Find the 10" term of the sequence, using the solution to the recurrence relation you just found.

Show your work here: 

a10= 

 

3. Solve the recurrence relation. Given:
9 = 3
0
●
q=
a
a = (6)a
n
= 6
n-1
n-2
Show your work in the space provided.
a.
7-1
= 6a + 7a
Find c, and c
+ (7)a,
2
II
7-2
2
r² − c¸r – c₂ = 0
b. Substitute c and
€2²
€₂
Show your work here:
into the following equation:
c. Identify a, b, and c in the quadratic equation.
Show your work here:
-b ± √b² - 4ac
2a
C=
d. Use the quadratic formula to find the two roots. Here is the quadratic formul
-b ± √b² - 4ac
2a
Transcribed Image Text:3. Solve the recurrence relation. Given: 9 = 3 0 ● q= a a = (6)a n = 6 n-1 n-2 Show your work in the space provided. a. 7-1 = 6a + 7a Find c, and c + (7)a, 2 II 7-2 2 r² − c¸r – c₂ = 0 b. Substitute c and €2² €₂ Show your work here: into the following equation: c. Identify a, b, and c in the quadratic equation. Show your work here: -b ± √b² - 4ac 2a C= d. Use the quadratic formula to find the two roots. Here is the quadratic formul -b ± √b² - 4ac 2a
e. Substitute two roots, r, and r.
1
Jauni
11
Show your work here:
f. Now substitute to find two equations, a and
you found from step e.
Show your work here:
a = 3=
P
X1
H
into the equation a = a₁ + a₂₂
P2
a = 6=
g. Add the two equations together find
a =
Remember to use the equation
h. What is the solution to the recurrence relations?
and a2
i. Find the 10th term of the sequence, using the solution to the recurrence relation
you just found.
Show your work here:
Transcribed Image Text:e. Substitute two roots, r, and r. 1 Jauni 11 Show your work here: f. Now substitute to find two equations, a and you found from step e. Show your work here: a = 3= P X1 H into the equation a = a₁ + a₂₂ P2 a = 6= g. Add the two equations together find a = Remember to use the equation h. What is the solution to the recurrence relations? and a2 i. Find the 10th term of the sequence, using the solution to the recurrence relation you just found. Show your work here:
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