[Euler-Fermat]

1.$\lim_{n \to \infty}a_n = \sqrt{9n^2+1} +\sqrt{n^2+6n+1} -4n = 3n+n-4n+3 = 3 $
2. $a_n =a_1+(n-1)d $
$\lim_{n \to \infty}(\frac{a_n-a_1}{n}) = 8 $
$\lim_{n \to \infty}(\frac{(n-1)d}{n}) =8 $
$\therefore d=8$
$a_6+a_8 = 100 ......(1)$
$a_8 = a_6 +2d แทนค่าลงไปใน (1)$
$ได้ a_6 = 42$
$a_99 = a_6+93d = 42+744 = 786 $