Question

There are four arithmetic means between $2$ and $-18$ The means are

• A. -4, -7, -10, -13
• B. 1,-4, -7,-10
• C. -2,-5,-9,-13
• D. -2,-6,-10,-14

Answer 1

Answer: (D)

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.;
$\Rightarrow -18=2+5b$
$\Rightarrow 5b=-20$
$\Rightarrow b=-4$
Hence, $X_1=2+b=2+(-4)=-2$;
$X_2=2+2b=2-8=-6$
$X_3=2+3b=2-12=-10$,
$X_4^3=2+4b=2-16=-14$
he required means are $-2,-6,-10,-14$