Folklore

A hundred non-zero numbers are written in a row on the board. It is known that each number, except the first and the last, is the product of the two adjacent numbers. The first number is 7. What is the last number?
Given the conditions $a_{2}=a_{1} a_{3}, a_{3}=a_{2} a_{4}, \ldots, a_{99}=a_{98} a_{100}$. By multiplying two consecutive equations, we get $a_{k} a_{k+3}=1$, which means $a_{k+3}=1 / a_{k}$. Therefore,

$a_{k+6}=a_{k}$. Hence, $a_{1}=a_{7}=\ldots=a_{97}=7$, and $a_{100}=1 / a_{97}=1 / 7$.

## Answer

$1 / 7$