Chapter 1, Problem 6NT

NOW TRY THIS

Here is the Fibonacci sequence:

$n$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$	…
$F_n$	$1$	$1$	$2$	$3$	$5$	$8$	$13$	$21$	$34$	$55$	$89$	$144$	$233$	$377$	$610$	…

There are some interesting patterns. Look at the number $F_3=2$. Every $3\text{rd}$ number is a multiple of $2:\left(2,8,34,144,610,\mathrm{...}\right)$. Find other patterns for every fourth number, every fifth number, and conjecture a pattern for every $n\text{th}$ number.