Question #306323

Given an=an−1−6an−2 where a0=1 a2=5

a.) list the first 10 terms of the sequence

b.) find a closed form(solve the recurrence relations) 


1
Expert's answer
2022-03-07T23:03:02-0500

Solution


Given that


{a_n} = {a_{n - 1}} - 6{a_{n - 2}}\


And, a0=1{a_0} = 1 , a2=5{a_2} =5


For n=2n=2


{a_2} = {a_{2 - 1}} - 6{a_{2 - 2}}\\ {a_2} = {a_{1}} - 6{a_{0}}\


using, a0=1{a_0} = 1 , a2=5{a_2} =5


5=a16(1)a1=115 = {a_{1}} - 6(1)\rightarrow {a_{1}}=11


Similarly, for For n=3n=3

a3=a26a1a3=56(11)a3=61{a_3} = {a_{2}} - 6{a_{1}}\\ {a_3} = 5 - 6(11)\\ {a_3} =-61


Similarly, for For n=4n=4

a4=a36a2a4=616(5)a4=91{a_4} = {a_{3}} - 6{a_{2}}\\ {a_4} = -61-6(5)\\ {a_4} =-91


Continuing in the same way, we get the next few terms, which are tabulated as shown below.









Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS