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Answer :
Final answer:
To find the 3rd term of the AP, we first establish the relationship between the terms using the given information, solve for the first term a and common difference d, and then use these values to find the 3rd term. The 3rd term of the AP is 7/8.
Explanation:
Finding the 3rd Term of an Arithmetic Progression (AP)
To find the 3rd term of the AP in this problem, let's denote the first term as a and the common difference as d. The nth term of an AP is given by a + (n-1)d. Therefore, the 4th term is a + 3d and is given as 3 times the first term, which is 3a. So, we have a + 3d = 3a, which simplifies to 3d = 2a.
Next, the 7th term is a + 6d and the 3rd term is a + 2d. The problem states the 7th term exceeds the 3rd term by 1. Therefore, (a + 6d) - (a + 2d) = 1, which simplifies to 4d = 1. Using the equation 3d = 2a, we determine a by substituting d = 1/4 to get 3(1/4) = 2a, which results in a = 3/8. The 3rd term is then a + 2d = 3/8 + 2(1/4)
= 3/8 + 1/2
= 7/8.
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