Question

Insert $18$ arithmetic means between $-35x$ and $3x$.

Answer 1

The sequence will form an A.P with

$a=-35x$ and $a_{20}=3x$

$a_n=a+(n-1)d\Rightarrow a_{20}=a+(20-1)d\Rightarrow 3x=-35x+19d\Rightarrow d=2xa+d,a+2d+a+3d...........a+18d\Rightarrow -33x,-31x,-29x.......,x$