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Answer :
Final answer:
To find the 28th term of the arithmetic progression, we use the given sums of its terms to calculate the first term and the common difference. Then, applying these values, the 28th term is determined through the AP's nth term formula.
Explanation:
The question relates to finding the 28th term of an arithmetic progression (AP) given the sum of the first 7 terms and the sum of the next 7 terms. The sum of the first 7 terms (S7) is 63, and the sum of the next 7 terms (S14 - S7) is 161. Let the first term be a and the common difference be d. The formula for the sum of the first n terms of an AP is Sn = n/2 [2a + (n-1)d]. Using the given information:
- S7 = 7/2 [2a + 6d] = 63
- S14 - S7 = 161 or S14 = 161 + 63 = 224
- S14 = 14/2 [2a + 13d] = 224
Solving these two equations, we find the values of a and d. The 28th term (T28) of an AP is given by Tn = a + (n-1)d. Substituting the found values of a and d gives us the 28th term.
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