Write an explicit formula for a_(n), the n^("th ") term of the sequence 24,-12,6,dots Answer: a_(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 24, -12, 6, ... has a common ratio between consecutive terms, as each term is obtained by multiplying the previous term by a constant. To find this constant, we can divide the second term by the first term: -12 / 24 = -1/2. Similarly, dividing the third term by the second term gives 6 / -12 = -1/2. Since the ratio is consistent, the sequence is geometric.Use Explicit Formula: Use the explicit formula for a geometric sequence, a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. For the sequence 24, -12, 6, ..., the first term, a_1, is 24 and the common ratio, r, is -1/2.Substitute Values: Substitute the values of a_1 and r into the formula to write an expression to describe the sequence. The expression for the sequence 24, -12, 6, ... is a_n = 24 * (-1/2)^(n-1).

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
24,-12,6,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $24,-12,6, \ldots$ $\newline$ Answer: $a_{n}=$

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Math Problems

Algebra 2

Write a formula for an arithmetic sequence

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

24,-12,6, \ldots

\newline

Answer:

a_{n}=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $24, -12, 6, \ldots$ has a common ratio between consecutive terms, as each term is obtained by multiplying the previous term by a constant. To find this constant, we can divide the second term by the first term: $-12 / 24 = -1/2$ . Similarly, dividing the third term by the second term gives $6 / -12 = -1/2$ . Since the ratio is consistent, the sequence is geometric.
Use Explicit Formula: Use the explicit formula for a geometric sequence, $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio. For the sequence $24, -12, 6, \ldots$ , the first term, $a_1$ , is $24$ and the common ratio, $r$ , is $-\frac{1}{2}$ .
Substitute Values: Substitute the values of $a_1$ and $r$ into the formula to write an expression to describe the sequence. The expression for the sequence $24, -12, 6, extellipsis$ is a_n = 24 imes (-rac{1}{2})^{(n-1)}.