Question

Find $t_n$ for the following $A.P.s$
$4,9,14,\mathrm{19.....}$

Answer 1

General term $AP$ is given by

$t_n=a+nd$

$t_1=a+2d$

$4=a+d------\left(1\right)$

$t_2=a+2d$

$9=a+2d-----\left(2\right)$

Subtract $\left(1\right)$ and $\left(2\right)$,

$9-4(2d-d)+(a-a)$

$a+d=4$
$a+5=4$

$\therefore a-1$

$\therefore t_n=5_n-1$