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The sum of the first 7 terms of an arithmetic progression (AP) is 63, and the sum of its next 7 terms is 161. Find the 28th term of the AP.

Answer :

Final answer:

To find the 28th term of an arithmetic progression, we need to find the common difference by solving a system of equations. Once we have the common difference, we can use the formula to find the 28th term.

Explanation:

To find the 28th term of the arithmetic progression (AP), we need to first find the common difference (d). We are given that the sum of the first 7 terms is 63, so we can use the formula for the sum of an AP: Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, and d is the common difference. For the first 7 terms, we have 63 = (7/2)(2a + 6d).Similarly, for the next 7 terms, we have 161 = (7/2)(2(a+7d) + 6d). Now we have a system of two equations with two variables (a and d). Solving these equations simultaneously will give us the values of a and d. Once we have a and d, we can find the 28th term of the AP using the formula: an = a + (n-1)d.

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