If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?
-3
Let the first term be a and the common difference be d. The 5th, 7th, and 13th terms of the AP are a + 4d, a + 6d, and a + 12d, respectively. For these to be in GP, the ratio of consecutive terms must be constant. After applying the GP condition, the ratio of the first term to the common difference comes out to be -3.
Similar Questions
- If \(a, b, c\) are in AP; \(b, c, d\) are in GP; \(c, d, e\) are in HP, then which of the following is/are correct?
1. \(a, c\) and \(e\) are in GP
2. \(\frac{1}{a}, \frac{1}{c}, \frac{1}{e}\) are in GP
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Important Questions from Arithmetic Progression
If the arithmetic mean of a, b, c is \(\rm \frac M 3\) and \(\rm \frac{1}{a} + \frac{1}{b} = -\frac{1}{c} \) , then the arithmetic mean of a 2, b 2, c 2 is
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How many natural numbers lie between 3 and 200 which are divisible by 7?
The arithmetic mean of 16 student's scores is 320. Find the sum of these scores.
How many three-digit numbers are divisible by 5?
