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

Calculate 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 arithmetic and each term is 6 less than the term before it. The explicit formula for 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 Values: We know the first term a_1 is 37 and the common difference d is -6. Now we can substitute these values into the formula to find the explicit formula for a_n. Calculation: a_n = 37 + (n - 1)(-6)Distribute -6: Simplify the formula by distributing the -6 into the parentheses. Calculation: a_n = 37 - 6(n - 1)Multiply Terms: Further simplify the formula by multiplying out the terms inside the parentheses. Calculation: a_n = 37 - 6n + 6Combine Like Terms: Combine like terms to get the final explicit formula for the nth term of the sequence. 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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Math Problems

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}=

Calculate 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 arithmetic and each term is $6$ less than the term before it. The explicit formula for 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 Values: We know the first term $a_1$ is $37$ and the common difference $d$ is $-6$ . Now we can substitute these values into the formula to find the explicit formula for $a_n$ . $\newline$ Calculation: $a_n = 37 + (n - 1)(-6)$
Distribute $-6$ : Simplify the formula by distributing the $-6$ into the parentheses. $\newline$ Calculation: $a_n = 37 - 6(n - 1)$
Multiply Terms: Further simplify the formula by multiplying out the terms inside the parentheses. $\newline$ Calculation: $a_n = 37 - 6n + 6$
Combine Like Terms: Combine like terms to get the final explicit formula for the nth term of the sequence. $\newline$ Calculation: $a_n = 43 - 6n$