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NDA 2 2024 Maths, question 7

Topic: Algebra

Q7

If pp times the pthpth term of an AP is equal to qq times the qthqth term (p≠q)(p\ne q), then what is the (p+q)th(p+q)th term equal to?

  1. (a) 00Correct answer
  2. (b) p+qp+q
  3. (c) pqpq
  4. (d) pq(p+q)pq(p+q)

Solution.

Answer: (a) 00

  1. Write the nth term as a+(n−1)d.
  2. The condition gives p[a+(p−1)d]=q[a+(q−1)d].
  3. Subtract and factor: (p−q)[a+(p+q−1)d]=0.
  4. Because p≠q, the bracket, which is the (p+q)th term, is zero.