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
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=
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