Question

Find the common difference of the following ap.hence find the 5th term. √3,√26,√75,√147,......

Answer 1

$a_1 = \sqrt{3}$
$a_2 = \sqrt{27} = 3 \sqrt{3}$
$a_3 = \sqrt{75} = 5 \sqrt{3}$
$a_4 = \sqrt{147} = 7 \sqrt{3}$

Therefore $d = a_2 - a_1$
$d = 3 \sqrt{3} - \sqrt{3}$$d = 2 \sqrt{3}$

Therfore $a_5 = a_4 + d$
$a_5 = 7 \sqrt{3} +2 \sqrt{3}$
$a_5 = 9 \sqrt{3} = \sqrt{243}$