Question

If 6 arithmetic means are inserted between 1 and 9/2 , find the 4th arithmetic mean

Answer 1

Answer:

Fourth arithmetic mean is 3

Step-by-step explanation:

Let $A_1,A_2 ,A_3 ,A_4 , A_5, A_6$ be 6 six arithmetic between 1 and 9/2

Let d be the common difference.

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

Now,

Fourth arithmetic mean

$=A_4\\\\=1+4d\\\\=1+4(\frac{1}{2})\\\\=1+2\\\\=3$