How do you find d for the arithmetic series with s17=-170 and a1=2?

Aug 25, 2016

$d = - 1.5$

Explanation:

We use the formula s_n = n/2(2a + (n - 1)d)) to find the sum of an arithmetic series.

In our problem, we have that $n = 17$, ${s}_{17} = - 170$ and $a = 2$. We are looking for $d$.

$- 170 = \frac{17}{2} \left(2 \left(2\right) + \left(17 - 1\right) d\right)$

$- 170 = \frac{17}{2} \left(4 + 16 d\right)$

$- 170 = 34 + 136 d$

$- 204 = 136 d$

$d = - 1.5$

Hopefully this helps!