Answer
$a_{1}=5, a_{2}=6,a_{n}=a_{n-2}+a_{n-1}$
The next three terms: $45,73$ and $118$.
Work Step by Step
There is no common difference. So, the sequence is not arithmetic.
There is no common ratio. So, the sequence is not geometric.
Lets look for the pattern. We note that
$a_{1}+a_{2}=5+6=11=a_{3}$
$a_{2}+a_{3}=6+11=17=a_{4}$ and so on.
Beginning with the third term, each term is the sum of the previous two terms.
So, a recursive rule for the sequence is
$a_{1}=5, a_{2}=6,a_{n}=a_{n-2}+a_{n-1}$
The next three terms are:
$a_{6}=a_{4}+a_{5}=17+28=45$
$a_{7}=a_{5}+a_{6}=28+45=73$
$a_{8}=a_{6}+a_{7}=45+73=118$.
