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# CAT 2017 [slot 1] Question with solution 31

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
Option: 1
Explanation:

The seventh term of an AP = a + 6d. Third term will be a + 2d and second term will be a + 16d. We are given that
$(a + 6d)^2 = (a + 2d)(a + 16d)$
=> $a^2$ + $36d^2$ + 12ad = $a^2 + 18ad + 32d^2$
=> $4d^2 = 6ad$
=> $d:a = 3:2$