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If p times the p th term of an AP is q times the q th term, then what is the (p+q) th term equal to?

Options

  1. Ap+q
  2. Bp q
  3. C1
  4. D0

Correct answer

D. 0

Step-by-step solution

aligned p^ t h & =a+(p-1) d q^ t h & =a+(q-1) d aligned By hypothesis aligned & a p+ (p^2-p ) d=a q+ (q^2-q ) d & (a p-a q)= (q^2-q-p^2+p ) d & or a(p-q)= [(p-q)- (p^2-q^2 ) ] d & (p+q) th =a+(p+q-1) d & =[1-(p+q)] d-[1-(p+q)] d=0 aligned

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