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Prove that the sum of n …

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Prove that the sum of n numbers between a and b such that the resulting series becomes AP is n(a+b)÷2
  • 1 answers

Dεερακ Ȿιηɠꜧ 4 years, 3 months ago

Sum of A.P. = T₁ + T₂ + T₃.....T
Given AP = a , T₂ , T₃....., ,b
Sum of Given A.P. =[ a+ (a+d)+(a+2d)+(a+3d)+..+(a+nd)]
A.P. = [(b-nd)+...+(b-3d)+(b-2d)+(b-d)+b]
By Adding both A.P. we get 2(A.P.) = na+nb + 0d
A.P. = n(a+b)/2
Sum of terms = ½n(a+b)
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