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

Class 10

Math

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Arithmetic Progressions

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150

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
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
543
150

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