Question

Insert $17$ arithmetic means between $3\frac{1}{2}$ and $-41\frac{1}{2}$.

Answer 1

The sequence will from an A.P with

$a=3\frac{1}{2}=\frac{7}{2}$ and $a_{19}=-41\frac{1}{2}=-\frac{83}{2}$

$t_n=a+(n-1)d\Rightarrow t_{19}=a+(19-1)d\Rightarrow -\frac{83}{2}=\frac{7}{2}+18d\Rightarrow d=-\frac{5}{2}a+d,a+2d+a+3d...........a+19d\Rightarrow 1,-\frac{3}{2},-\mathrm{4...........}-39$