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Question 31 : If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is :
Given that the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th 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 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is :"
Choice A is the correct answer
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