124*. A checker can move in one direction along a strip divided into cells, moving either to the adjacent cell or skipping one cell in a single move. In how many ways can it move 10 cells?
$\triangle$ A checker can move one cell in 1 way, two cells in 2 ways, three cells in $-1+2=3$ ways, four cells in $-3+2=5$ ways, five cells in $-3+5=8$ ways, and so on. In fact, the Fibonacci sequence (see the solution to problem 12) is formed, which is defined by the recurrence relation

$$
a_{n}=a_{n-1}+a_{n-2}(n \in N, n>2)
$$

and initial conditions $a_{1}=1$ and $a_{2}=2$. We find its 10th term.

Answer: $89$.