If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

Options

A. `x=y lt z`
B. `x= y gt z`
C. `x lt z lt y`
D. `x gt z lt y`

Answer

C

Explanation

`x=a+b = 14 pm 0.14 rArr % `error `= (0.14)/(14) xx 100 = 1% , y = a-b= 2 pm 0.14 rArr % ` error `= (0.14)/(2) xx 100 = 7% `
`z= ab = 48 pm 0.96 rArr %` error `= (0.96)/(48) xx 100 = 2% `. Therefore order of % error is `x lt z lt y`