Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.1 Sequences and Series - 14.1 Exercise Set - Page 894: 25

$a_{1}=(1)^2+2=3$ $a_{2}=(2)^2+2=6$ $a_{3}=(3)^2+2=11$ $a_{4}=(4)^2+2=18$ $a_{10}=(10)^2+2=102$ $a_{15}=(15)^2+2=227$

If we want to find a term, we have to substitute $n$ by its index: $a_{1}=(1)^2+2=3$ $a_{2}=(2)^2+2=6$ $a_{3}=(3)^2+2=11$ $a_{4}=(4)^2+2=18$ $a_{10}=(10)^2+2=102$ $a_{15}=(15)^2+2=227$