Question

if p arithmetic mean are inserted between a and b,prove that

Answer 1

\[d=\frac{ b-a }{ p+1 }\]

Answer 2

if p arithmetic mean are inserted between a and b,prove that \[d=\frac{ b-a }{p+1}\]

Answer 3

i check it but only ^^^^^ this is given

Answer 4

@jim_thompson5910

Answer 5

oh i think i know what it's saying

if p = 1, then you have 1 arithmetic mean

d = (b-a)/(p+1)

d = (b-a)/(1+1)

d = (b-a)/2

So the distance from that arithmetic mean to either 'a' or 'b' is (b-a)/2


Notice how this is the average of two values

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if p = 2, then you have 2 arithmetic means

d = (b-a)/(p+1)

d = (b-a)/(2+1)

d = (b-a)/3

So the distance from the left most arithmetic mean to 'a' is (b-a)/3

The distance from the left most arithmetic to the right most arithmetic mean is (b-a)/3

The distance from the right most arithmetic mean to b is (b-a)/3


The value (b-a)/3 basically divides the interval from 'a' to 'b' into 3 equal chunks


Etc etc

this works for any positive integer p

Answer 6

thank @jim_thompson5910