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in Arithmetic Progression by (71.1k points)
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Prove that the sum of `n` arithmetic means between two numbers in `n` times the single A.M. between them.

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Let `A_1,A_2,A_3,..,A_n`
Am between a,b
`AP->a,A_1,A_2,...,A_n,b`
`b=a+(n+2-1)d`
`d=(b-a)/(n+1)-(A)`
Now,
`A_1+A_2+...+A_n=n/2[A_1+A_n]`
`a+b=A_1+A_n`
`A_1+A_22+...+A_n=n/2[a+b]`
`=n((a+b)/2)`
=n(AM between a and b).

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