Question

If $17$ arithmetic means are inserted between $\frac{7}{2}$ and $\frac{-83}{2},$ then the $17^{th}$ arithmetic mean is

• A. $-19$
• B. $-29$
• C. $-39$
• D. $-49$

Answer 1

Answer: (C)

Let $d$ be the common difference. Then
$d=\frac{\left(-\frac{83}{2}\right)-\left(\frac{7}{2}\right)}{18}=\frac{-5}{2}$
So, the $17^{th}$ mean is given by
$-\frac{83}{2}-\left(-\frac{5}{2}\right)=-\frac{83}{2}+\frac{5}{2}=-\frac{78}{2}=-39$