Arithmetic Progression

Relevant wiki: Arithmetic Progressions

The sum of the first $n$ terms of an arithmetic progression is given by the formula, $s=\dfrac{n}{2}(a_1+a_n)$ where $n$ = number of terms, $a_1$ = first term and $a_n$ = $n^{th}$ term

Substituting, we get

$216=\dfrac{n}{2}(n+2n)$

$432=3n^2$

$n^2=144$

Extracting the square root of both sides, we get

$n=±12$

$n=-12$ is rejected

So,

$n=12$

The $n^{th}$ term of an arithmetic progression is given by the formula, $a_n=a_1+(n-1)d$ .

Substituting, we get

$24=12+(11d)$

$12=11d$

Finally,

$d=\dfrac{12}{11}=1.09$ $\boxed{\text{answer}}$