Question

Find :

(i) 10th term of the A.P. 1, 4, 7, 10, .....

(ii) 18th term of the A.P. $\sqrt{2},3\sqrt{2},5\sqrt{2},\dots \dots$

(iii) nth term of the A.P. 13, 8, 3, -2, .....

Answer 1

(i) 10th term of the A.P. 1, 4, 7, 10, ......

Here, 1st term $=a_1=1$

and common difference d = 4 - 1 = 3

We know $an=a_1+(n-1)d$

$\therefore a_{10}=a_1+(10-1)d$

$=1+(10-1)3\Rightarrow 28$

(ii) 18th term of the A.P. $\sqrt{2},3\sqrt{2},5\sqrt{2},\dots \dots$

Here, 1st term $a_1=\sqrt{2}$

and d = common difference $=2\sqrt{2}$

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

$a_{18}=\sqrt{2}+2\sqrt{2}\left(17\right)=35\sqrt{2}$

(iii) nth term of the A.P. 13, 8, 3, -2, ......

Here, $a_1=13$

d = -5

$\therefore a_n=a+(n-1)d$

$=13+(n-1)(-5)$

$=-5n+18$