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Find the three arithmetic means between -4 and 16

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SOLUTION

This question simply means we should find the three terms between the -4 and 6 to make this an arithmetic sequence

Let x, y and z be these 3 terms or arithmetic means.

So the arithmetic sequence will be


-4,x,y,z,16

Let d be the common difference, so

From nth term of an arithmetic sequence


\begin{gathered} T_n=a+(n-1)d \\ T_2=a+(2-1)d \\ T_2=a+1d \end{gathered}

So x will be


x=a+1d

Hence, y and z becomes


\begin{gathered} y=a+2d \\ z=a+3d \end{gathered}

And the 5th term which is 16 will be given as


16=a+4d

Now note that the first term a = -4. From the equation above the common difference d becomes


\begin{gathered} 16=a+4d \\ 16=-4+4d \\ 16+4=4d \\ 20=4d \\ d=(20)/(4) \\ d=5 \end{gathered}

The common difference is 5,

Hence x is


\begin{gathered} x=a+1d \\ x=-4+1(5) \\ x=-4+5 \\ x=1 \end{gathered}

y becomes


\begin{gathered} y=a+2d \\ y=-4+2(5) \\ y=-4+10 \\ y=6 \end{gathered}

z becomes


\begin{gathered} z=a+3d \\ z=-4+3(5) \\ z=-4+15 \\ z=11 \end{gathered}

Hence, the answer is 1, 6 and 11

User Aldanor
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