If the ratio of 5th terms of two Arithmetic Progressions is same as the ratio of their 9th terms, what is the ratio of their common differences?
Explanation:
Let the first term and common difference of first AP be a1 and d1, while that of second AP be a2 and d2.
⇒ a1+4d1a2+4d2 = a1+9d1a2+9d2
⇒ a1a2 + 9a1d2 + 4a2d1 + 36d1d2 = a1a2 + 4a1d2 + 9a2d1 + 36d1d2
⇒ 5a1d2 = 5a2d1
⇒ d1 : d2 = a2 : a2
Hence, option (e).
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