In an arithmetic progression, if \( S_{40} = 1030 \) and \( S_{12} = 57 \), then \( S_{30} - S_{10} \) is equal to:
Show Hint
- \( 510 \)
- \( 525 \)
- \( 515 \)
- \( 505 \)
The Correct Option is A
Solution and Explanation
In an arithmetic progression, the sum of the first \( n \) terms is given by the formula: \[ S_n = \frac{n}{2} (2a + (n - 1) d), \] where \( a \) is the first term and \( d \) is the common difference. We are given \( S_{40} = 1030 \) and \( S_{12} = 57 \).
From these, we can solve for \( a \) and \( d \). Then, we calculate \( S_{30} - S_{10} \) using the same formula.
Final Answer: \( S_{30} - S_{10} = 510 \).
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