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Question 31 : If the square of the 7^th term of an arithmetic progression with positive common difference equals the product of the 3^rd and 17^th terms, then the ratio of the first term to the common difference is :

1. 2 : 3
2. 3 : 2
3. 3 : 4
4. 4 : 3

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Progressions

Given that the square of the 7^th term of an arithmetic progression with positive common difference equals the product of the 3^rd and 17^th terms
(a + 6d)² = (a + 2d)(a + 16d)
We have to find the ratio of the first term to the common difference
⟹ (a + 6d)² = (a + 2d)(a + 16d)
⟹ a² + 12d + 36 = a² + 2ad + 16ad + 32d²
⟹ 4d² + 12 ad – 18 ad = 0
⟹ 4d² = 6ad
⟹ 4d = 6a
⟹ \\frac{a}{d}) = \\frac{4}{6}) = \\frac{2}{3})
The ratio of first term to the common difference is 2 : 3

The question is "If the square of the 7^th term of an arithmetic progression with positive common difference equals the product of the 3^rd and 17^th terms, then the ratio of the first term to the common difference is :"

Hence, the answer is 2 : 3

Choice A is the correct answer