Question

Find 18th term of theA.P $\sqrt{2},3\sqrt{2},5\sqrt{2}$

Answer 1

Given A.P is

$\sqrt{2},3\sqrt{2},5\sqrt{2},.....$

first term of this A.P is $a_1=\sqrt{2}$

second term of this A.P is $a_2=3\sqrt{2}$

common difference of an A.P is given by

$(i.e.,d=a_{n+1}-a_n)$

putting n=1 in above equation

$d=a_2-a_1=3\sqrt{2}-\sqrt{2}=\sqrt{2}(3-1)=2\sqrt{2}$

hence common difference for this A.P is $d=2\sqrt{2}$

the nth term of an A.P is given by.

$a_n=a_1+(n-1)d$

hence, for calculating 10th term of A.P $a_{18}$ put n=18 in above equation

$a_{18}=a_1+(18-1)d$

$a_{18}=\sqrt{2}+17\times 2\sqrt{2}$

$a_{18}=\sqrt{2}+34\sqrt{2}$

$a_{18}=\sqrt{2}(1+34)$

$a_{18}=35\sqrt{2}$