Question

Insert three arithmetic means between -16 and 4

Answer 1

To answer this question we will use the following formulas to compute n arithmetic means between 'a' and 'b':

`\begin{gathered} A_1=a+(b-a)/(n+1), \\ A_2=a+2\cdot(b-a)/(n+1), \\ \ldots \\ A_n=a+n\cdot(b-a)/(n+1)\text{.} \end{gathered}`

Substituting n=3, a=-16, and b=4 we get:

`\begin{gathered} A_1=-16+(4-(-16))/(3+1), \\ A_2=-16+2\cdot(4-(-16))/(3+1), \\ A_3=-16+3\cdot(4-(-16))/(3+1)\text{.} \end{gathered}`

Simplifying the above results we get:

`\begin{gathered} A_1=-16+(4+16)/(4)=-16+(20)/(4)=-11, \\ A_2=-16+2\cdot(4+16)/(4)=-16+(40)/(4)=-6, \\ A_3=-16+3\cdot(4+16)/(4)=-16+(60)/(4)=-1. \end{gathered}`

Answer: -11, -6, and -1.