Final answer:
To find the sum of the first 28 terms of an arithmetic progression with the 14th term being 55 and the sum of the first 13 terms being 351, we first determine the first term and common difference of the A.P. Using these, we can then apply the sum formula to calculate the sum of the first 28 terms.
Step-by-step explanation:
The question asks us to find the sum of the first 28 terms of an arithmetic progression (A.P.) given that the 14th term is 55 and the sum of the first 13 terms is 351. First, we need to determine the common difference (d) and the first term (a) of the A.P. Since the sum of the first n terms (Sn) of an A.P. is given by the formula Sn = n/2(2a + (n-1)d), we can set up an equation using the given S13 = 351. We also know the nth term of an A.P. is given by an = a + (n-1)d, and we have a14 = 55. Solving these two equations will give us the values for a and d.
Once we have a and d, we can then find the sum of the first 28 terms using the Sn formula again with n = 28. To find the requested sum, we would calculate S28 = 28/2(2a + 27d). With the calculated values of a and d, substituting them will yield the correct sum of the first 28 terms of the A.P.