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

Options

  1. A0
  2. Bp+q
  3. Cp q
  4. Dp q(p+q)

Correct answer

A. 0

Step-by-step solution

Suppose 'a' and 'd' be the first term and common difference of AP respectively. aligned & n ^ th term = T _ n = a +( n -1) d & ( p + q )^ th term = T _ p + q = a +( p + q -1) d ....(i) aligned Given, p T _ p = q T _ q aligned & p [ a +( p -1) d ]= q [ a +( q -1) d ] & ( p - q )[ a +( p + q -1) d ]=0 & [ a +( p + q -1) d ]=0 p q & T _ p + q =0 from ( i ) aligned

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