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)
Solution
Given that
{a_n} = {a_{n - 1}} - 6{a_{n - 2}}\
And, ,
For
{a_2} = {a_{2 - 1}} - 6{a_{2 - 2}}\\ {a_2} = {a_{1}} - 6{a_{0}}\
using, ,
Similarly, for For
Similarly, for For
Continuing in the same way, we get the next few terms, which are tabulated as shown below.
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