Question

What does n arthimetic means between two numbers exactly mean?

Answer 1

@ikram002p @dan815 @ganeshie8 @UnkleRhaukus

Answer 2

\[

\frac{a+b}{2}
\]

Answer 3

"N" arithmetic means

Answer 4

it just means to insert \(n\) numbers between the given two numbers so that it forms an AP with \(n+2\) terms.

Answer 5

that all those N arithmetic means are evenly spaced between a and b
if we have

a, q,w,e,r,t,y,b
then 'a' to 'q' distance = 'q' to 'w' distance = ... so on = 'y' to 'b' distance.

in other words,
a, N ARITHMETIC MEANS, b form an arithmetic series

Answer 6

They are arithmetic means of what

Answer 7

let me rephrase your question :
why `arithmetic sequence` is called `arithmetic sequence` ? whats so arithmetic about it ?

Answer 8

a, q,w,e,r,t,y,b

q is the AM of a and w
w is the AM of q and e
and so on...

also you can say
'w' is the AM of 'a' and 'r'
...

so there is no specific answer to whos AMs are those

Answer 9

This has some histroy attached to it @ganeshie8

Answer 10

each term in an AP is arithmetic mean of its adjacent terms - so thats the reason our ancestors named it as `arithmetic(means) sequence`

Answer 11

Note that the concept `arithmetic mean` was invented before the `sequences`

Answer 12

a , b ,c are in AP
b is the arithmetic mean of a and c

so what are the n arithmetic means " means" of

Answer 13

there is no single answer to that

Answer 14

That's what my sir told me , but i wanted the logic lol

Answer 15

so in your sequence you have `1` arithmetic mean between `a` and `c`

cuz b = (a+c)/2

Answer 16

arithmetic mean :-
they use the word arithmatic as a sighn to addition operation
and mean means the avg of that sumation of two numbers

Answer 17

So it has no logic
Just cooking up a A.P between two numbers

Answer 18

http://openstudy.com/study#/updates/53b25d04e4b072c759d72251 can any 1 explain this

Answer 19

^
in same way
for a,b,c,d
there are `2` AMs between a and d

b is the AM of a and c
c is the AM of b and d

Answer 20

well @No.name its not a logic its a concept

Answer 21

b and c are AM's of a and d ? r

Answer 22

whatever @ikram002p

Answer 23

b and c are AM's of a and d ? <<< NO

b is the AM of a and c
c is the AM of b and d

Answer 24

Oh i see

Answer 25

lol dont whatever me :P

Answer 26

b, c are two arithmetic means between a and d. yes.

Answer 27

yeah , but not arithmetic means of "a" and "b" I finally understand this "CONCEPT"

Answer 28

correct,
in a, q,w,e,r,t,y,b, there are 6 AMs between a and b, but not necessarily of a and b

Answer 29

yeah, one arithmetic mean of a, d will be given by (a+d)/2 which is also equal to (b+c)/2.

Answer 30

so he meant, (4+1)/2 = (3+2)/2 = 2.5

Answer 31

ohk!