Find an explicit formula for the arithmetic sequence 81,54,27,0,dots". " Note: the first term should be a(1). a(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 81, 54, 27, 0, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Find First Term and Difference: Determine the first term (a1) and the common difference (d) of the sequence. The first term a1 is 81. To find the common difference, subtract the second term from the first term: d = 54 - 81 = -27.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, an = a1 + (n-1)d, where a1 is the first term and d is the common difference. For this sequence, a1 = 81 and d = -27.Substitute Values: Substitute the values of a1 and d into the formula to write an expression to describe the sequence. The expression for the sequence 81, 54, 27, 0, ... is an = 81 + (n-1)(-27).Simplify Expression: Simplify the expression to find the explicit formula. an = 81 - 27(n-1) = 81 - 27n + 27 = 108 - 27n.

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Algebra 2

Write a formula for an arithmetic sequence

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Q. Find an explicit formula for the arithmetic sequence

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81,54,27,0, \ldots \text {.. }

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Note: the first term should be

a

(

1

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a(n) = $\square$

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $81, 54, 27, 0, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Find First Term and Difference: Determine the first term ( $a_1$ ) and the common difference ( $d$ ) of the sequence. The first term $a_1$ is $81$ . To find the common difference, subtract the second term from the first term: $d = 54 - 81 = -27$ .
Use Explicit Formula: Use the explicit formula for an arithmetic sequence, $a_n = a_1 + (n-1)d$ , where $a_1$ is the first term and $d$ is the common difference. For this sequence, $a_1 = 81$ and $d = -27$ .
Substitute Values: Substitute the values of $a_{1}$ and $d$ into the formula to write an expression to describe the sequence. The expression for the sequence $81, 54, 27, 0, \ldots$ is $a_{n} = 81 + (n-1)(-27)$ .
Simplify Expression: Simplify the expression to find the explicit formula. $a_{n} = 81 - 27(n-1) = 81 - 27n + 27 = 108 - 27n$ .