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The ratio of the 11th term to the 17th term of an arithmetic progression (AP) is 3:4. What is the common difference (d) of the AP?

a) 2
b) 3
c) 4
d) 5

Answer :

Final answer:

To find the common difference (d) of an arithmetic progression (AP), we can use the formula: d = (nth term - first term) / (n - 1). In this case, we are given the ratio of the 11th term to the 17th term as 34. Solving the equation, we find that d = 2.

Explanation:

To find the common difference (d) of an arithmetic progression (AP), we can use the formula:


d = (nth term - first term) / (n - 1)


In this case, we are given the ratio of the 11th term to the 17th term as 34. Let's assume the first term is a and the common difference is d. Then, the 11th term would be a + 10d and the 17th term would be a + 16d.


Using the given information, we can set up the equation:


(a + 10d) / (a + 16d) = 34


Solving this equation, we find that d = 2.

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