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 p times the pth term of an AP is equal to q times the qth term \((p \neq q)\), then what is the \((p+q)\)th term equal to?
- What is the common difference?
- In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is \(p^2: q^2\). Which one of the following is correct?
- What is the sum of all five terms?
- 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
Select the correct answer using the code given below : - How many terms are identical in the two APs \(19, 21, 23, ...\) up to 110 terms and \(19, 22, 25, 28, ...\) up to 75 terms?
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
How many two-digit numbers are divisible by 3 ?
A person saves Rs. 1000 more than he did the previous year. If he saves Rs. 2000 in the first year, in how many years will he save Rs. 170000?
A car starts with a speed of 60 km/h with its speed increasing every one hour by 5 km/h. In how many hours will it cover 435 kms?
How many natural numbers lie between 3 and 200 which are divisible by 7?
