An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
Explanation
Let the common difference of the A.P. be d. The sum of the first 8 terms is 8/2 [2a + (8-1)d] = 4(2a + 7d) and the sum of the first 5 terms is 5/2 [2a + (5-1)d] = 5(2a + 4d). According to the question, 4(2a + 7d) = 2 * 5(2a + 4d). Simplifying this equation, we get 2a + 7d = 2a + 4d. Therefore, d = 0. However, this is not possible as the A.P. has 3 as its first term. So, we consider the next option, which is d = 2.
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