Write an explicit formula for a_(n), the n^("th ") term of the sequence 144,24,4,dots Answer: a_(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 144, 24, 4, ... has a common ratio between consecutive terms, so it is a geometric sequence.Use Explicit Formula: Use the explicit formula for a geometric sequence, an = a1 * r^(n-1), where a1 is the first term and r is the common ratio. For the sequence 144, 24, 4, ..., the first term, a1, is 144 and the common ratio, r, can be found by dividing the second term by the first term: r = 24 / 144 = 1/6.Substitute Values: Substitute the values of a1 and r into the formula to write an explicit formula for the nth term of the sequence. The expression for the sequence 144, 24, 4, ... is an = 144 * (1/6)^(n-1).

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
144,24,4,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $144,24,4, \ldots$ $\newline$ Answer: $a_{n}=$

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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

144,24,4, \ldots

\newline

Answer:

a_{n}=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $144$ , $24$ , $4$ , ... has a common ratio between consecutive terms, so it is a geometric sequence.
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 $144, 24, 4, \ldots$ , the first term, $a_1$ , is $144$ and the common ratio, $r$ , can be found by dividing the second term by the first term: $r = \frac{24}{144} = \frac{1}{6}$ .
Substitute Values: Substitute the values of $a_{1}$ and $r$ into the formula to write an explicit formula for the $n$ th term of the sequence. The expression for the sequence $144, 24, 4, \ldots$ is $a_{n} = 144 \times (1/6)^{n-1}$ .