10. Show that an = : 2n5n is also a solution to the recurrence relation an = 7an-1-10an-2. What would the initial conditions need to be for this to be the closed formula for the sequence?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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For the Recurrence relation. i was doing this steps:

an = 2n - 5n

WTS : an = 7an-1 - 10an-2

Lets prove LHS = RHS

2n - 5n = 7an-1 - 10an-2

= 7(2n-1 - 5n-1) - 10(2n-2 - 5n-2)

= 7 X 2n-1  - 7 X - 5n-1 - 10 X 2n-2  + 10 X 5n-2

=  "? "  from this line how can i solve this problem & prove LHS = RHS  (2n - 5n = 2n - 5n )

 

Please answer this ques using my steps.please and solve this problem (try to show the work line by line )

          

10. Show that an = 2″ − 5″ is also a solution to the recurrence relation
an = 7an-1-10an-2. What would the initial conditions need to be for
this to be the closed formula for the sequence?
Transcribed Image Text:10. Show that an = 2″ − 5″ is also a solution to the recurrence relation an = 7an-1-10an-2. What would the initial conditions need to be for this to be the closed formula for the sequence?
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