Answer
$a_n=\dfrac{15}{4}+\dfrac{9}{4}n$
Work Step by Step
We know that the general formula of an arithmetic sequence is given by
$a_n= a_1+(n-1) d$ ...(1)
Here, we have $a_1+4d=15$ ..(2)
$a_1+8d=24$ ..(3)
Now, we will have to subtract equation (2) from (3).
$9=4d \implies d=\dfrac{9}{4}$
Equation (1) gives: $a_n= 6+(n-1) \dfrac{9}{4}$
$a_n=\dfrac{24-9}{4}+\dfrac{9}{4}n$
Thus, we find that the nth term is: $a_n=\dfrac{15}{4}+\dfrac{9}{4}n$
