Question

If Sm=mr+1/2m(m-1)S,where Sm denotes the sum of first m terms of an AP then the common difference​

Answer 1

Given : Sm=mr+(1/2)m(m-1)S

Sm denotes the sum of first m terms of an AP

To Find : common difference​

Solution:

S₁ = a₁    

Sm=mr+(1/2)m(m-1)S

m = 1

=> S₁ =  (1)r + (1/2)(1)(1 - 1)S

=> S₁ = r  + 0

=> S₁ = r

S₁ = a₁    

=> a₁ = r

S₂ = a₁  + a₂

=> S₂ =r  + a₂

S₂ = (2)r + (1/2)(2)(2 - 1)S

=> S₂ = 2r + S

r  + a₂  =  2r + S

=> a₂  =  r + S

d = a₂ - a₁

=> d =  r + S - r

=> d  = S

common difference​ = S

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