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.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 the sequence 81, 54, 27, 0, ..., the first term, a1, is 81 and we need to find the common difference, d.Calculate common difference: Calculate the common difference, d, by subtracting the second term from the first term: d = 54 - 81 = -27.Write expression for sequence: 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 for sequence: Simplify the expression to get the final explicit formula for the arithmetic sequence. an = 81 - 27(n-1) = 81 - 27n + 27 = 108 - 27n.

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

a(n)=

Find an explicit formula for the arithmetic sequence $\newline$ $81,54,27,0, \ldots \text {.. }$ $\newline$ Note: the first term should be $a$ ( $1$ ). $\newline$ $a(n)=$

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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

\newline

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

\newline

Note: the first term should be

a

(

1

\newline

a(n)=

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.
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 the sequence $81, 54, 27, 0, \ldots$ , the first term, $a_1$ , is $81$ and we need to find the common difference, $d$ .
Calculate common difference: Calculate the common difference, $d$ , by subtracting the second term from the first term: $d = 54 - 81 = -27$ .
Write expression for sequence: 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 for sequence: Simplify the expression to get the final explicit formula for the arithmetic sequence. $a_n = 81 - 27(n-1) = 81 - 27n + 27 = 108 - 27n$ .