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In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms?

Options

  1. Am x(m+n) n-1
  2. Bm x(m+n) 1-n
  3. Cn x(m+n) m-1
  4. Dn x(m+n) 1-m

Correct answer

B. m x(m+n) 1-n

Step-by-step solution

a=xS n=0 n 2 [2 a+(n-1) d]=02 a+(n-1) d=0( n 0) Sum of next m terms = Sum of (m+n) terms - (Sum of first n - terms) S_ m+n = m+n 2 [2 a+(m+n-1) d]-0= m+n 2 [2 x- 2 x(m+n-1) n-1 ]=(m+n) x [1- m+n- ]=(m+n) x[ n-1-m-n+1 ]= -m(m+n) x n-1 = m(m+n) x 1-n .

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