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Write an equation to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term. \newline–5, –15, –45, …–5, \, –15, \, –45, \, \dots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____\_\_\_\_)n−1^{n - 1}

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Q. Write an equation to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term. \newline–5, –15, –45, …–5, \, –15, \, –45, \, \dots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____\_\_\_\_)n−1^{n - 1}
  1. Sequence Type: We have: \newline–55, –1515, –4545, ... \newlineIs the given sequence geometric or arithmetic? \newline–55, –1515, –4545, ... \newlineHere, each term is multiplied by a common ratio.\newlineThe given sequence is geometric.
  2. Determine Values: –5,–15,–45,…–5, –15, –45, \ldots \newlineDetermine the values of a1a_1 and rr of the sequence. \newlineFirst term: a1=–5a_1 = –5 \newlineCommon ratio: r=–15–5=3r = \frac{–15}{–5} = 3
  3. Expression for ana_n: We have: \newlinea1=−5a_1 = -5 \newliner=3r = 3 \newlineDetermine an expression to describe ana_n.\newlineSubstitute −5-5 for a1a_1 and 33 for rr.\newlinean=a1(r)n−1a_n = a_1 (r)^{n - 1} \newlinean=−5(3)n−1a_n = -5(3)^{n-1}

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