Question
21. Given the sequence \( \{-1,3,7,11, \ldots\} \), find \( a_{25} \). A. 103 B. 99 C. 95 D. 91
Ask by Wheeler Pena. in Guam
Mar 12,2025
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Answer
The 25th term \( a_{25} \) is 95.
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Beyond the Answer
The given sequence is an arithmetic sequence where the first term \( a_1 = -1 \) and the common difference \( d = 4 \) (since \( 3 - (-1) = 4 \), \( 7 - 3 = 4 \), and \( 11 - 7 = 4 \)). The general formula for the \( n \)-th term of an arithmetic sequence is given by: \[ a_n = a_1 + (n-1) \cdot d \] For \( n = 25 \): \[ a_{25} = -1 + (25-1) \cdot 4 = -1 + 24 \cdot 4 = -1 + 96 = 95 \] Thus, the answer is: C. 95