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Answer :
Final answer:
To find the arithmetic progression (AP) given the sum of the first 10 terms and the last 15 terms in a sequence. The correct option is a) 5, 7, 9, ..., 103.
Explanation:
Arithmetic progression (AP):
Given: Sum of first 10 terms = 210, Sum of last 15 terms = 2565
- Using the formula for the sum of an AP: Sum = n/2[(2a + (n-1)d)], where a is the first term, d is the common difference, and n is the number of terms.
- Apply the given information to form the equations: 10/2[2a + 9d] = 210 and 15/2[2b + 14d] = 2565.
- Solve the equations simultaneously to find: a = 5, d = 2.
Hence, the AP is 5, 7, 9, ..., 103. The correct option is a) 5, 7, 9, ..., 103.
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