Write an explicit formula for a_(n), the n^("th ") term of the sequence 35,28,21,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 consecutive terms. We do this by subtracting any term from the term that follows it. Calculation: 28 - 35 = -7General Form of nth Term: The common difference is -7, which means this is an arithmetic sequence where each term is 7 less than the previous term. The general form of the nth term 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 into Formula: We know the first term a_1 is 35 and the common difference d is -7. Now we can substitute these values into the formula. Calculation: a_n = 35 + (n - 1)(-7)Simplify Formula: Simplify the formula by distributing the common difference -7 through the parentheses. Calculation: a_n = 35 - 7(n - 1)Multiply Out Terms: Further simplify the formula by multiplying out the terms inside the parentheses. Calculation: a_n = 35 - 7n + 7Combine Like Terms: Combine like terms to get the final explicit formula for the nth term. Calculation: a_n = 42 - 7n

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
35,28,21,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $35,28,21, \ldots$ $\newline$ 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

35,28,21, \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 consecutive terms. We do this by subtracting any term from the term that follows it. $\newline$ Calculation: $28 - 35 = -7$
General Form of nth Term: The common difference is $-7$ , which means this is an arithmetic sequence where each term is $7$ less than the previous term. The general form of the $n$ th term 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 into Formula: We know the first term $a_1$ is $35$ and the common difference $d$ is $-7$ . Now we can substitute these values into the formula. $\newline$ Calculation: $a_n = 35 + (n - 1)(-7)$
Simplify Formula: Simplify the formula by distributing the common difference $-7$ through the parentheses. $\newline$ Calculation: $a_n = 35 - 7(n - 1)$
Multiply Out Terms: Further simplify the formula by multiplying out the terms inside the parentheses. $\newline$ Calculation: $a_n = 35 - 7n + 7$
Combine Like Terms: Combine like terms to get the final explicit formula for the nth term. $\newline$ Calculation: $a_n = 42 - 7n$