Write an explicit formula that represents the sequence defined by the following recursive formula: a_(1)=4" and "a_(n)=a_(n-1)+5 Answer: a_(n)=

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Write an explicit formula that represents the sequence defined by the following recursive formula:  a_(1)=4" and "a_(n)=a_(n-1)+5 Answer:  a_(n)=

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Identify Pattern: To find the explicit formula for the sequence, we need to determine a pattern that can be applied directly to find any term in the sequence without having to find all the previous terms.Find First Terms: Let's start by finding the first few terms of the sequence using the recursive formula: a_(1) = 4 (given) a_(2) = a_(1) + 5 = 4 + 5 = 9 a_(3) = a_(2) + 5 = 9 + 5 = 14 a_(4) = a_(3) + 5 = 14 + 5 = 19 From this pattern, we can see that each term is 5 more than the previous term.Analyze Relationship: Now, let's look at the relationship between the term number (n) and the value of each term: a_(1) = 4 = 4 + 5(1 - 1) a_(2) = 9 = 4 + 5(2 - 1) a_(3) = 14 = 4 + 5(3 - 1) a_(4) = 19 = 4 + 5(4 - 1) We can see that the term value is equal to the first term (4) plus 5 times (n - 1).Determine Explicit Formula: The pattern suggests that the explicit formula for the nth term is: a_(n) = 4 + 5(n - 1) This formula allows us to calculate the value of any term directly.Verify Formula: To verify that this formula is correct, let's test it with n = 5: a_(5) = 4 + 5(5 - 1) = 4 + 5(4) = 4 + 20 = 24 Now, let's check it with the recursive definition: a_(5) = a_(4) + 5 = 19 + 5 = 24 Both methods give us the same result, confirming that our explicit formula is correct.

Write an explicit formula that represents the sequence defined by the following recursive formula: $\newline$ $a_{1}=4 \text { and } a_{n}=a_{n-1}+5$ $\newline$ Answer: $a_{n}=$

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Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=4 and an=an−1+5 a_{1}=4 \text { and } a_{n}=a_{n-1}+5 a1​=4 and an​=an−1​+5\newlineAnswer: an= a_{n}= an​=

Write an explicit formula that represents the sequence defined by the following recursive formula: $\newline$ $a_{1}=4 \text { and } a_{n}=a_{n-1}+5$ $\newline$ Answer: $a_{n}=$