Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises - Page 605: 32

$a_1 = 2$ $a_2 = 17$ $a_3 = 82$ $a_4 = 257$ Diverges. The terms are increasing without a bound as $n$ increases.

$a_n = n^4 + 1$ $a_1 = 1^4 + 1 =2$ $a_2 = 2^4 + 1 = 17$ $a_3 = 3^4 + 1 = 82$ $a_4 = 4^4 + 1 =257$ Since the values of the sequence are increasing without a bound, the sequence is diverging.