If three times the 9th term of an A.P is equal to five times its 1 | Filo
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Arithmetic Progressions

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If three times the $$9$$th term of an A.P is equal to five times its $$13$$th term, then which of the following term will be zero.

  1. $$26$$th
  2. $$19$$th
  3. $$21$$st
  4. $$36$$th
Correct Answer: Option(b)
Solution: According to the question $$3(a+8d)=5(a+12d)$$
$$\Rightarrow 3a+24d=5a+60d$$
$$\Rightarrow 2a+36d=0$$
$$\Rightarrow a+18d=0$$
$$\Rightarrow a+(19-1)d=0$$
Hence $$19^{th}$$ term is zero
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