Write an explicit formula for a_(n), the n^("th ") term of the sequence 72,-24,8,dots Answer: a_(n)=

Determine Pattern: To find the explicit formula for the nth term of the sequence, we first need to determine the pattern of the sequence. We can do this by examining the relationship between consecutive terms.Identify Geometric Sequence: The second term is -24, which is -1/3 of the first term 72. The third term is 8, which is -1/3 of the second term -24. This suggests that each term is -1/3 times the previous term, indicating that the sequence is geometric.Use Geometric Sequence Formula: For a geometric sequence, the nth term 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. In this sequence, a_1 = 72 and r = -1/3.Write Explicit Formula: Now we can write the explicit formula for the nth term of the sequence using the values of a_1 and r. The formula is a_n = 72 * (-1/3)^(n-1).

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
72,-24,8,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $72,-24,8, \ldots$ $\newline$ Answer: $a_{n}=$

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Algebra 2

Transformations of quadratic functions

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

72,-24,8, \ldots

\newline

Answer:

a_{n}=

Determine Pattern: To find the explicit formula for the $n$ th term of the sequence, we first need to determine the pattern of the sequence. We can do this by examining the relationship between consecutive terms.
Identify Geometric Sequence: The second term is $-24$ , which is $-\frac{1}{3}$ of the first term $72$ . The third term is $8$ , which is $-\frac{1}{3}$ of the second term $-24$ . This suggests that each term is $-\frac{1}{3}$ times the previous term, indicating that the sequence is geometric.
Use Geometric Sequence Formula: For a geometric sequence, the nth term 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. In this sequence, $a_1 = 72$ and $r = -\frac{1}{3}$ .
Write Explicit Formula: Now we can write the explicit formula for the $n$ th term of the sequence using the values of $a_1$ and $r$ . The formula is $a_n = 72 \times (-\frac{1}{3})^{(n-1)}$ .