$a _ { n } = ( - 1 ) ^ { n + 5}$

Name: $a _ { n } = ( - 1 ) ^ { n + 5}$
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Question

Quizplus · Accepted Answer

The sequence $a_n = (-1)^{n+5}$ alternates in sign because the exponent $n+5$ changes parity (odd/even) as $n$ increases. For $n=1$ to $n=5$, the exponents are 6, 7, 8, 9, and 10, respectively. Even exponents result in 1, and odd exponents result in -1, leading to the pattern 1, -1, 1, -1, 1.

an=(−1)n+5a _ { n } = ( - 1 ) ^ { n + 5}an​=(−1)n+5

$a _ { n } = ( - 1 ) ^ { n + 5}$