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

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Find Terms: To find the explicit formula for the sequence, we need to determine the pattern of the sequence based on the given recursive formula. Let's start by finding the first few terms of the sequence. a_(1) = 1 (given) a_(2) = -4a_(1) = -4(1) = -4 a_(3) = -4a_(2) = -4(-4) = 16 a_(4) = -4a_(3) = -4(16) = -64 We can see that the sequence is alternating in sign and each term is 4 times the previous term in magnitude.Identify Pattern: Now, let's look for a pattern in the exponents of 4 for each term. a_(1) = 4^0 (since 4^0 = 1) a_(2) = -4^1 a_(3) = 4^2 a_(4) = -4^3 We can see that the exponent of 4 is one less than the term number and the sign alternates with each term.Sign Pattern: To account for the alternating sign, we can use (-1) raised to a power that will alternate the sign for each term. We can use the term number minus 1 as the exponent for (-1) to alternate the sign. So, the pattern for the sign is (-1)^(n-1).Combine Patterns: Combining the pattern for the magnitude of 4 and the alternating sign, we can write the explicit formula for the sequence as: a_(n) = (-1)^(n-1) * 4^(n-1) This formula will give us the nth term of the sequence by plugging in the value of n.

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

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