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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
  • a)
    2:3
  • b)
    3:2
  • c)
    3:4
  • d)
    4:3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the square of the 7th term of an arithmetic progression with posit...
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)
=> a2 + 36d2 + 12ad = a2+ 18ad + 32d2
=> 4d2 = 6ad
=>d: a = 3:2
we have been asked about a: d. Hence, it would be 2:3
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Most Upvoted Answer
If the square of the 7th term of an arithmetic progression with posit...
Solution:

Given:
- Let the arithmetic progression be a, a + d, a + 2d, a + 3d, ..., where a is the first term and d is the common difference.
- The 7th term: a + 6d
- The 3rd term: a + 2d
- The 17th term: a + 16d

Given condition:
- (a + 6d)^2 = (a + 2d)(a + 16d)

Expanding the terms:
- a^2 + 12ad + 36d^2 = a^2 + 18ad + 32d^2
- Simplifying the equation: 6ad = 4d^2
- Simplifying further: a/d = 2/3

Ratio of the first term to the common difference:
- a:d = 2:3
Therefore, the ratio of the first term to the common difference is 2:3 (option 'A').
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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 isa) 2:3b) 3:2c) 3:4d) 4:3Correct answer is option 'A'. Can you explain this answer?
Question Description
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