Write an explicit formula that represents the sequence defined by the following recursive formula: a_(1)=125" and "a_(n)=(1)/(5)a_(n-1) Answer: a_(n)=

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Write an explicit formula that represents the sequence defined by the following recursive formula:  a_(1)=125" and "a_(n)=(1)/(5)a_(n-1) Answer:  a_(n)=

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Identify First Term & Relationship: Identify the first term and the recursive relationship. The first term of the sequence is given as a_(1)=125. The recursive formula is given as a_(n)=(1)/(5)a_(n-1), which means each term is one-fifth of the previous term.Recognize Sequence Type: Recognize the type of sequence. Since each term is a constant fraction of the previous term, this is a geometric sequence.Determine Common Ratio: Determine the common ratio (r) of the geometric sequence. The common ratio r is the factor by which we multiply one term to get the next term. From the recursive formula a_(n)=(1)/(5)a_(n-1), we can see that r=(1)/(5).Write Explicit Formula: Write the explicit formula for a geometric sequence. The explicit formula for a geometric sequence is a_(n)=a_(1)*r^(n-1), where a_(1) is the first term and r is the common ratio.Substitute Values: Substitute the values of a_(1) and r into the explicit formula. We have a_(1)=125 and r=(1)/(5). Substituting these values into the formula gives us a_(n)=125*(1/5)^(n-1).Simplify Expression: Simplify the expression if possible. The expression a_(n)=125*(1/5)^(n-1) is already in its simplest form, so no further simplification is needed.

Write an explicit formula that represents the sequence defined by the following recursive formula: $\newline$ $a_{1}=125 \text { and } a_{n}=\frac{1}{5} a_{n-1}$ $\newline$ Answer: $a_{n}=$

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Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=125 and an=15an−1 a_{1}=125 \text { and } a_{n}=\frac{1}{5} a_{n-1} a1​=125 and an​=51​an−1​\newlineAnswer: an= a_{n}= an​=

Write an explicit formula that represents the sequence defined by the following recursive formula: $\newline$ $a_{1}=125 \text { and } a_{n}=\frac{1}{5} a_{n-1}$ $\newline$ Answer: $a_{n}=$