Question

The ratio of the 5th term to the 18th term of the apil in 2:3.find the ratio of 5thto21th.

Answer 1

It is given that the ratio of 5th term to 18th term is 2:3
let the first term of the ap be a nd the common difference be d
$\frac{a + (5 - 1)d}{a + (18 - 1)d} = \frac{2}{3} \\ \frac{a +4d}{a + 17d} = \frac{2}{3} \\ 3a + 12d = 2a + 34d \\ a = 22d ........(i) \\ we \: hv \: to \: find \: the \: ratio \: of \: 5th \: term \: to \: 21st \: term \: \\ \frac{a + 4d}{a + 20d} \\ by(i) \\ \frac{22d + 4d}{22d + 20d} = \frac{26d}{42d} \\ hence \: the \: ratio \: is \: \ \frac{13}{21}$

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