Answered: 10. Show that an = : 2n5n is also a…

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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

For the Recurrence relation. i was doing this steps:

a_n = 2ⁿ - 5ⁿ

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

Lets prove LHS = RHS

2ⁿ - 5ⁿ = 7a_n-1- 10a_n-2

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

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

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