Question

Find out the common difference of the arithmetic progression whose $9^{th}$ term is $19$ and also whose first term is $3$.

Answer 1

Now, it is given that the $t_9=19$ . Also $a=3$. To find the value of d, we can use the formula

$t_n=a+(n-1)d$

Thus, $19=3+(9-1)d$

Or, $16=8d$

Thus, $d=2$

Thus, the common difference of the required A.P. is $2$.