Write an explicit formula that represents the sequence defined by the following recursive formula: a_(1)=5" and "a_(n)=a_(n-1)-3 Answer: a_(n)=

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Write an explicit formula that represents the sequence defined by the following recursive formula:  a_(1)=5" and "a_(n)=a_(n-1)-3 Answer:  a_(n)=

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Understand the recursive formula: Understand the recursive formula. The given recursive formula is a_(1)=5 and a_(n)=a_(n-1)-3. This means that each term is 3 less than the previous term, starting with the first term being 5.Determine first few terms: Determine the first few terms of the sequence. To find the explicit formula, it's helpful to write out the first few terms of the sequence using the recursive formula: a_(1) = 5 a_(2) = a_(1) - 3 = 5 - 3 = 2 a_(3) = a_(2) - 3 = 2 - 3 = -1 a_(4) = a_(3) - 3 = -1 - 3 = -4 ... We can see that each term is decreasing by 3 from the previous term.Look for pattern: Look for a pattern to derive the explicit formula. From the pattern in Step 2, we can see that each term is 3 less than the previous term. This suggests that the nth term is the first term minus 3 times (n-1), because there are (n-1) steps from the first term to the nth term.Write explicit formula: Write the explicit formula based on the pattern. The explicit formula for the nth term is: a_(n) = a_(1) - 3(n-1) Since we know a_(1) = 5, we can substitute that into the formula: a_(n) = 5 - 3(n-1)Simplify formula: Simplify the explicit formula. Now we simplify the formula: a_(n) = 5 - 3n + 3 a_(n) = 8 - 3n This is the explicit formula for the given recursive sequence.

Write an explicit formula that represents the sequence defined by the following recursive formula: $\newline$ $a_{1}=5 \text { and } a_{n}=a_{n-1}-3$ $\newline$ Answer: $a_{n}=$

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Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=5 and an=an−1−3 a_{1}=5 \text { and } a_{n}=a_{n-1}-3 a1​=5 and an​=an−1​−3\newlineAnswer: an= a_{n}= an​=

Write an explicit formula that represents the sequence defined by the following recursive formula: $\newline$ $a_{1}=5 \text { and } a_{n}=a_{n-1}-3$ $\newline$ Answer: $a_{n}=$