Answer
a)
$a_{1}=1060$
$a_{2}=1123.60$
$a_{3}=1191.02$
$a_{4}=1262.48$
$a_{5}=1338.23$
b)
$a_{n}$ is divergent.
Work Step by Step
$a_{n}=1000(1.06)^{n}$
a)
$a_{1}=1000(1.06)=1060$
$a_{2}=1000(1.06)^{2}=1123.60$
$a_{3}=1000(1.06)^{3}=1191.02$
$a_{4}=1000(1.06)^{4}=1262.48$
$a_{5}=1000(1.06)^{5}=1338.23$
b)
$\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}(1000)(1.06)^{n}$
$=1000\lim\limits_{n \to \infty}(1.06)^{n}$
$=\infty$
Thus $a_{n}$ is divergent.
