Write an explicit formula for a_(n), the n^("th ") term of the sequence 27,-9,3,dots Answer: a_(n)=

Identify pattern in sequence: We first identify the pattern in the sequence. The sequence starts with 27 and each term is divided by -3 to get the next term: 27, -9, 3, ...Calculate ratio: This is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio. To find the ratio (r), we divide the second term by the first term: r = (-9) / 27 = -1/3.Use geometric sequence formula: The first term of the sequence, a_1, is 27. The nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.Substitute values into formula: Substituting the values of a_1 and r into the formula, we get a_n = 27 * (-1/3)^(n-1).Simplify if necessary: This is the explicit formula for the nth term of the sequence. It can be simplified further if necessary, but in this case, it is already in its simplest form.

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
27,-9,3,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $27,-9,3, \ldots$ $\newline$ Answer: $a_{n}=$

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Algebra 2

Convert between explicit and recursive formulas

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

27,-9,3, \ldots

\newline

Answer:

a_{n}=

Identify pattern in sequence: We first identify the pattern in the sequence. The sequence starts with $27$ and each term is divided by $-3$ to get the next term: $27, -9, 3, \ldots$
Calculate ratio: This is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio. To find the ratio $r$ , we divide the second term by the first term: $r = (-9) / 27 = -\frac{1}{3}$ .
Use geometric sequence formula: The first term of the sequence, $a_1$ , is $27$ . The $n$ th term of a geometric sequence is given by the formula $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Substitute values into formula: Substituting the values of $a_1$ and $r$ into the formula, we get $a_n = 27 \times (-\frac{1}{3})^{(n-1)}$ .
Simplify if necessary: This is the explicit formula for the $n$ th term of the sequence. It can be simplified further if necessary, but in this case, it is already in its simplest form.