Answer
The first five terms are:
$a_1= \sqrt2$
$a_2 = \sqrt{2+\sqrt2}$
$a_3 = \sqrt{2+\sqrt{2+\sqrt2}}$
$a_4 = \sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}$
$a_5= \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}}$
Work Step by Step
Use the given recursive formula to find the next four terms:
$a_1= \sqrt2$
$a_2 = \sqrt{2+a_1} = \sqrt{2+\sqrt2}$
$a_3 = \sqrt{2+a_2} = \sqrt{2+\sqrt{2+\sqrt2}}$
$a_4 = \sqrt{2+a_3} = \sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}$
$a_5= \sqrt{2+a_4} = \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}}$
