Question

insert three arithmetic means between -16 and 14

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Numbers are -16 and 14}$

$\underline{\textsf{To find:}}$

$\textsf{Three arithmetric means between -16 and 14}$

$\underline{\textsf{Solution:}}$

$\textsf{Let}\;\mathsf{A_1,A_2,A_3}\,\textsf{be the three arithmetic means between -16 and 14}$

$\textsf{Let d be the common difference}$

$\textsf{Then,}$

$\mathsf{A_1=-16+d}$

$\mathsf{A_2=-16+2d}$

$\mathsf{A_3=-16+3d}$

$\mathsf{14=-16+4d}$

$\implies\mathsf{4d=14+16}$

$\implies\mathsf{4d=30}$

$\implies\mathsf{d=\dfrac{30}{4}}$

$\implies\mathsf{d=\dfrac{15}{2}}$

$\mathsf{A_1=-16+\dfrac{15}{2}=\dfrac{-32+15}{2}=\dfrac{-17}{2}}$

$\mathsf{A_2=-16+2(\dfrac{15}{2})=-16+15=-1}$

$\mathsf{A_3=-16+3(\dfrac{15}{2})=-16+\dfrac{45}{2}=\dfrac{-32+45}{2}=\dfrac{13}{2}}$

$\underline{\textsf{Answer:}}$

$\textsf{The three A.M between -16 and 14 are}$

$\mathsf{\dfrac{-17}{2},-1,\dfrac{13}{2}}$