Question

find 4 arithmetic means between 1/9 and 9​

Answer 1

Answer:

Fourth arithmetic mean is 3

Step-by-step explanation:

Let A_1,A_2 ,A_3 ,A_4 , A_5, A_6A

1

,A

2

,A

3

,A

4

,A

5

,A

6

be 6 six arithmetic between 1 and 9/2

Let d be the common difference.

\begin{gathered}A_1=1+d\\\\A_2=1+2d\\\\A_3=1+3d\\\\A_4=1+4d\\\\A_5=1+5d\\\\A_6=1+6d\\\\\frac{9}{2}=1+7d\\\\\frac{9}{2}-1=7d\\\\\frac{9-2}{2}=7d\\\\\frac{7}{2}=7d\\\\d=\frac{1}{2}\end{gathered}

A

1

=1+d

A

2

=1+2d

A

3

=1+3d

A

4

=1+4d

A

5

=1+5d

A

6

=1+6d

2

9

=1+7d

2

9

−1=7d

2

9−2

=7d

2

7

=7d

d=

2

1

Now,

Fourth arithmetic mean

\begin{gathered}=A_4\\\\=1+4d\\\\=1+4(\frac{1}{2})\\\\=1+2\\\\=3\end{gathered}

=A

4

=1+4d

=1+4(

2

1

)

=1+2

=3