Find the number of terms of this progression

Relevant wiki: Arithmetic Progressions

Using the formula $a_n=a_m+(n-m)d$ , we have

$-155=-35+(10-2)d$ $\color{#D61F06}\implies$ $d=-15$

Using again the formula, we have

$a_1=-35+(1-2)(-15)=-20$

Using the formula $s=\dfrac{n}{2}[2a_1+(n-1)d]$ , we have

$-1645=\dfrac{n}{2}[2(-20)+(n-1)(-15)]$

Simplifying this will end in a quadratic equation

$15n^2+25n-3290=0$

Using any method to solve for $n$ , we find that $n=\boxed{14}$ .

final equation (x)/(2)(-40+(x-1)-15)=-1645