Write an explicit formula for a_(n), the n^("th ") term of the sequence 5,7,9,dots Answer: a_(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 5, 7, 9, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference. For the sequence 5, 7, 9, ..., the first term, a_1, is 5 and the common difference, d, is 2.Substitute Values: Substitute the values of a_1 and d into the formula to write an expression to describe the sequence. The expression for the sequence 5, 7, 9, ... is a_n = 5 + (n-1) × 2.Simplify Expression: Simplify the expression. a_n = 5 + 2n - 2, which simplifies to a_n = 2n + 3.

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
5,7,9,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $5,7,9, \ldots$ $\newline$ Answer: $a_{n}=$

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Algebra 2

Write a formula for an arithmetic sequence

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

5,7,9, \ldots

\newline

Answer:

a_{n}=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $5, 7, 9, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Use Explicit Formula: Use the explicit formula for an arithmetic sequence, $a_n = a_1 + (n-1)d$ , where $a_1$ is the first term and $d$ is the common difference. For the sequence $5, 7, 9, \ldots$ , the first term, $a_1$ , is $5$ and the common difference, $d$ , is $2$ .
Substitute Values: Substitute the values of $a_1$ and $d$ into the formula to write an expression to describe the sequence. The expression for the sequence $5, 7, 9, \ldots$ is $a_n = 5 + (n-1) \times 2$ .
Simplify Expression: Simplify the expression. $a_n = 5 + 2n - 2$ , which simplifies to $a_n = 2n + 3$ .