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if a is the single A.M between two numbers a and b.s is the sum of n A.M s between them then s​​÷a depend on?

if a is the single A.M between two numbers a and b.s is the sum of n A.M s between them then s​​÷a depend on?

Grade:12th pass

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
7 years ago
A = (a+b)/2
A1, A2 , … An be the n AM’s between a and b then the common difference d is
b = a + (n+2-1)d => d = (b-a)/(n+1)

now evaluating the sum from A1 to An is
S = (n/2)(A1+An)
A1 = a+d, An = a+nd
A1+An = 2a + (n+1)d = a+b
hence
s = n (a+b)/2 = nA

thus it just depends on n infact is equal to n

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