CAT 2017 Question Paper | Quants Slot 1

The questions that come from Progression in CAT involves concept based on Arithmetic progressions and Geometric progressions. In CAT Exam, one can generally expect to get 1~2 questions from Progressions. In this question, we have to find the ratio of the first term to the common ratio. With some simple but very powerful ideas, one can cut down on a lot of work when it comes to progression.

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

Video Explanation

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

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