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

Determine First Term: To find the explicit formula for an arithmetic sequence, we need to determine the first term (a(1)) and the common difference (d). The first term is given as 81.Find Common Difference: Next, we need to find the common difference (d). This can be found by subtracting any term from the term that follows it. Subtracting the second term (54) from the first term (81) gives us the common difference. d = 81 - 54 d = 27Write Explicit Formula: Now that we have the first term (a(1) = 81) and the common difference (d = 27), we can write the explicit formula for the nth term of an arithmetic sequence, which is: a(n) = a(1) + (n - 1)dSubstitute Values: Substitute the values of a(1) and d into the formula to get the explicit formula for this specific sequence: a(n) = 81 + (n - 1)(27)Simplify Formula: Simplify the formula by distributing the common difference: a(n) = 81 + 27n - 27Combine Like Terms: Combine like terms to get the final explicit formula: a(n) = 27n + 54

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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 $81,54,27,0, \ldots$ $\newline$ Note: the first term should be $a(1)$ . $\newline$ $a(n) = \square$ $\newline$

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Algebra 2

Evaluate explicit formulas for sequences

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Q. Find an explicit formula for the arithmetic sequence

81,54,27,0, \ldots

\newline

Note: the first term should be

a(1)

\newline

a(n) = \square

\newline

Determine First Term: To find the explicit formula for an arithmetic sequence, we need to determine the first term ( $a(1)$ ) and the common difference ( $d$ ). The first term is given as $81$ .
Find Common Difference: Next, we need to find the common difference $d$ . This can be found by subtracting any term from the term that follows it. Subtracting the second term ( $54$ ) from the first term ( $81$ ) gives us the common difference. $\newline$ $d = 81 - 54$ $\newline$ $d = 27$
Write Explicit Formula: Now that we have the first term $a(1) = 81$ and the common difference $d = 27$ , we can write the explicit formula for the $n$ th term of an arithmetic sequence, which is: $\newline$ $a(n) = a(1) + (n - 1)d$
Substitute Values: Substitute the values of $a(1)$ and $d$ into the formula to get the explicit formula for this specific sequence: $\newline$ $a(n) = 81 + (n - 1)(27)$
Simplify Formula: Simplify the formula by distributing the common difference: $a(n) = 81 + 27n - 27$
Combine Like Terms: Combine like terms to get the final explicit formula: $a(n) = 27n + 54$