the ratio of the 5th term to 3rd term of an ap is 2:5. find the ratio of the 15th term to 7th term

Hi Sadia Hafeez,

Kindly find the solution to your query:

Let a = first term and d = common difference

$$\begin{gathered} \mathrm{now}, \frac{a_5}{a_3} = \frac{2}{5} \\ \Rightarrow \frac{(a + 4d)}{(a + 2d)}= \frac{2}{5} \\ \Rightarrow 5a + 20d = 2a + 4d \\ \Rightarrow 3a = -16d \\ \Rightarrow a = - \frac{16}{3}d ......\left(1\right) \\ \mathrm{now}, \frac{a_{15}}{a_7} = \frac{a + 14d}{a + 6d }= \frac{- {\displaystyle \frac{16}{3}}d + 14d}{-{\displaystyle \frac{16}{3}}d + 6d} = \frac{{\displaystyle \frac{26}{3}}d}{{\displaystyle \frac{2}{3}}d}= \frac{13}{1} \end{gathered}$$

So the desired ratio is 13:1

To practise with some more questions following are the links of the similar queries as asked by you:

https://www.meritnation.com/ask-answer/question/the-ratio-of-the-11th-term-to-the-8th-trem-of-an-ap-is-2-3/arithmetic-progressions/3938704

https://www.meritnation.com/ask-answer/question/1-the-sum-of-the-first-five-terms-of-an-ap-and-the-sum-of-t/arithmetic-progressions/3600056

Hope this information will clear your doubts about this topic.

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Regards,
Vandana