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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
7,1,-5,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $7,1,-5, \ldots$ $\newline$ Answer: $a_{n}=$

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Write equations of cosine functions using properties

Full solution

Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

7,1,-5, \ldots

\newline

Answer:

a_{n}=

Identify Arithmetic Sequence: The given sequence is arithmetic because the difference between consecutive terms is constant. To find the common difference, subtract the second term from the first term. $\newline$ Common difference $d = 1 - 7 = -6$
Find Common Difference: The $n$ th term of an arithmetic sequence is given by the formula $a_n = a_1 + (n - 1)d$ , where $a_1$ is the first term and $d$ is the common difference. $\newline$ Here, $a_1 = 7$ and $d = -6$ .
Apply Explicit Formula: Substitute the values of $a_1$ and $d$ into the formula to get the explicit formula for the $n$ th term. $\newline$ $a_n = 7 + (n - 1)(-6)$ $\newline$ $a_n = 7 - 6n + 6$ $\newline$ $a_n = 13 - 6n$

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