Write an explicit formula for a_(n), the n^("th ") term of the sequence 37,31,25,dots Answer: a_(n)=

Determine Common Difference: To find the explicit formula for the nth term of the sequence, we first need to determine the common difference between the terms. We do this by subtracting any term from the term that follows it. Calculation: 31 - 37 = -6Arithmetic Sequence Formula: The common difference is -6, which means the sequence is an arithmetic sequence. The formula for the nth term of an arithmetic sequence is given by: a_n = a_1 + (n - 1)d where a_1 is the first term and d is the common difference.Substitute Known Values: Now we substitute the known values into the formula. The first term a_1 is 37 and the common difference d is -6. Calculation: a_n = 37 + (n - 1)(-6)Simplify Formula: Simplify the formula by distributing the common difference. Calculation: a_n = 37 - 6(n - 1)Multiply Out Terms: Further simplify the formula by multiplying out the terms. Calculation: a_n = 37 - 6n + 6Combine Like Terms: Combine like terms to get the final explicit formula. Calculation: a_n = 43 - 6n

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
37,31,25,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $37,31,25, \ldots$ $\newline$ Answer: $a_{n}=$

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Algebra 2

Transformations of quadratic functions

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

37,31,25, \ldots

\newline

Answer:

a_{n}=

Determine Common Difference: To find the explicit formula for the $n$ th term of the sequence, we first need to determine the common difference between the terms. We do this by subtracting any term from the term that follows it. $\newline$ Calculation: $31 - 37 = -6$
Arithmetic Sequence Formula: The common difference is $-6$ , which means the sequence is an arithmetic sequence. The formula for the $n$ th term of an arithmetic sequence is given by: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_1$ is the first term and $d$ is the common difference.
Substitute Known Values: Now we substitute the known values into the formula. The first term $a_1$ is $37$ and the common difference $d$ is $-6$ . $\newline$ Calculation: $a_n = 37 + (n - 1)(-6)$
Simplify Formula: Simplify the formula by distributing the common difference. $\newline$ Calculation: $a_n = 37 - 6(n - 1)$
Multiply Out Terms: Further simplify the formula by multiplying out the terms. $\newline$ Calculation: $a_n = 37 - 6n + 6$
Combine Like Terms: Combine like terms to get the final explicit formula. $\newline$ Calculation: $a_n = 43 - 6n$