Thank you for reporting, we will resolve it shortly
Q.
There are four arithmetic means between $2$ and $-18 $ The means are
Sequences and Series
Solution:
Let the means be $X_{1}, X_{2}, X_{3}, X_{4}$ and the common difference be $b$; then $2, X_{1}, X_{2}, X_{3}, X_{4},-18$ are in A.P.;
$\Rightarrow -18=2+5 b $
$\Rightarrow 5 b=-20$
$ \Rightarrow b=-4$
Hence, $X_{1}=2+b=2+(-4)=-2$;
$X_{2}=2+2 b=2-8=-6$
$X_{3}=2+3 b=2-12=-10$,
$X_{4}^{3}=2+4 b=2-16=-14$
he required means are $-2, -6, -10, -14$