given that the first term of an Ap is 7 and its 10th term is twice the second term. calculate the sum of the 28 term.

given that the first term of an Ap is 7 and its 10th term is twice the second term.calculate the 19th term, the sum of the 28 term and the common different between the 9th and the 6th term..

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To find the sum of the 28 terms of an arithmetic progression (AP), we need to first determine the common difference (d) between the terms. Once we have the common difference, we can apply the formula for the sum of an arithmetic series.

From the given information, we know that the first term (a1) is 7.
Let's assume that the second term (a2) is x.

We are also given that the 10th term (a10) is twice the second term (2x).

Using the formula for an arithmetic sequence:
a10 = a1 + (10 - 1) * d
2x = 7 + 9d

Since we have two equations with two variables, we can solve for both x and d.

Next, substitute the assumed value for a2 into the second equation:
2x = 7 + 9d

Substituting x = 7 + 9d/2 into the first equation:
2(7 + 9d/2) = 7 + 9d
14 + 9d = 7 + 9d
14 = 7

This equation is not valid, which means there is no unique solution for x and d. Therefore, the given information is not consistent and does not correspond to a valid arithmetic progression.

As a result, we cannot find the sum of the 28 terms given the given information.

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