Write an explicit formula for a_(n), the n^("th ") term of the sequence 27,23,19,dots Answer: a_(n)=

Identify Terms: To find the explicit formula for the nth term of an arithmetic sequence, we need to identify the first term (a_1) and the common difference (d).First Term and Difference: The first term of the sequence is 27. This is given directly by the sequence.Calculate Common Difference: To find the common difference, we subtract the second term from the first term: 23 - 27 = -4. The common difference is -4.Use Explicit Formula: The explicit formula for an arithmetic sequence is given by a_n = a_1 + (n - 1)d. We will use this formula with our identified values for a_1 and d.Substitute Values: Substitute the values into the formula: a_n = 27 + (n - 1)(-4).Simplify Formula: Simplify the formula: a_n = 27 - 4n + 4.Combine Like Terms: Combine like terms: a_n = 31 - 4n.

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
27,23,19,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $27,23,19, \ldots$ $\newline$ Answer: $a_{n}=$

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Precalculus

Convert a recursive formula to an explicit formula

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

27,23,19, \ldots

\newline

Answer:

a_{n}=

Identify Terms: To find the explicit formula for the $n$ th term of an arithmetic sequence, we need to identify the first term ( $a_1$ ) and the common difference ( $d$ ).
First Term and Difference: The first term of the sequence is $27$ . This is given directly by the sequence.
Calculate Common Difference: To find the common difference, we subtract the second term from the first term: $23 - 27 = -4$ . The common difference is $-4$ .
Use Explicit Formula: The explicit formula for an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$ . We will use this formula with our identified values for $a_1$ and $d$ .
Substitute Values: Substitute the values into the formula: $a_n = 27 + (n - 1)(-4)$ .
Simplify Formula: Simplify the formula: $a_n = 27 - 4n + 4$ .
Combine Like Terms: Combine like terms: $a_n = 31 - 4n$ .