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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

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Correct Answer - Option 1 : 2 : 3

Calculation:

⇒ 3rd term = a + 2d

⇒ 7th term = a + 6d

⇒ 17th term = a + 16d

⇒ (a + 6d)2 = (a + 2d) × (a + 16d)

⇒ By solving 6ad = 4d2 Since d > 0

⇒ 6a = 4d

⇒ a/d = 2/3

∴ The required result will be 2/3.

 nth terms of arithmetic progression = a + (n - 1) × d

Where a = First term, and d = Common difference

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