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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,… 81,54,27,0, \ldots \newlineNote: the first term should be a(1) a(1) .\newlinea(n)=□a(n) = \square\newline

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Q. Find an explicit formula for the arithmetic sequence 81,54,27,0,… 81,54,27,0, \ldots \newlineNote: the first term should be a(1) a(1) .\newlinea(n)=□a(n) = \square\newline
  1. Determine First Term: To find the explicit formula for an arithmetic sequence, we need to determine the first term (a(1)a(1)) and the common difference (dd). The first term is given as 8181.
  2. Find Common Difference: Next, we need to find the common difference dd. This can be found by subtracting any term from the term that follows it. Subtracting the second term (5454) from the first term (8181) gives us the common difference.\newlined=81−54d = 81 - 54\newlined=27d = 27
  3. Write Explicit Formula: Now that we have the first term a(1)=81a(1) = 81 and the common difference d=27d = 27, we can write the explicit formula for the nnth term of an arithmetic sequence, which is:\newlinea(n)=a(1)+(n−1)da(n) = a(1) + (n - 1)d
  4. Substitute Values: Substitute the values of a(1)a(1) and dd into the formula to get the explicit formula for this specific sequence:\newlinea(n)=81+(n−1)(27)a(n) = 81 + (n - 1)(27)
  5. Simplify Formula: Simplify the formula by distributing the common difference: a(n)=81+27n−27a(n) = 81 + 27n - 27
  6. Combine Like Terms: Combine like terms to get the final explicit formula: a(n)=27n+54a(n) = 27n + 54

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