# CAT 2017 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Progressions Questions | Question 31

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 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 :

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

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

##### Method of solving this CAT Question from Progressions

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