Write an explicit formula for a_(n), the n^("th ") term of the sequence 27,29,31,dots. Answer: a_(n)=

Identify pattern: Identify the pattern in the sequence. The sequence starts at 27 and each term increases by 2. This is an arithmetic sequence with a common difference of 2.Determine first term: Determine the first term (a_1) of the sequence. The first term of the sequence is 27.Find common difference: Determine the common difference (d) of the sequence. The common difference is the amount added to each term to get to the next term, which is 2.Write nth term formula: Write the formula for the nth term of an arithmetic sequence. The nth term a_n of an arithmetic sequence with the first term a_1 and common difference d is given by: a_n = a_1 + (n - 1)dSubstitute values: Substitute the values of a_1 and d into the formula. a_1 = 27 and d = 2, so the formula becomes: a_n = 27 + (n - 1) * 2Simplify formula: Simplify the formula. a_n = 27 + 2n - 2 a_n = 25 + 2n

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
27,29,31,dots.
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $27,29,31, \ldots$ . $\newline$ 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

27,29,31, \ldots

\newline

Answer:

a_{n}=

Identify pattern: Identify the pattern in the sequence. $\newline$ The sequence starts at $27$ and each term increases by $2$ . This is an arithmetic sequence with a common difference of $2$ .
Determine first term: Determine the first term ( $a_1$ ) of the sequence. $\newline$ The first term of the sequence is $27$ .
Find common difference: Determine the common difference $d$ of the sequence. $\newline$ The common difference is the amount added to each term to get to the next term, which is $2$ .
Write nth term formula: Write the formula for the nth term of an arithmetic sequence. $\newline$ The nth term $a_n$ of an arithmetic sequence with the first term $a_1$ and common difference $d$ is given by: $\newline$ $a_n = a_1 + (n - $1$)d
Substitute values: Substitute the values of $a_1$ and $d$ into the formula.$\newline$$a_1 = 27$ and $d = 2$, so the formula becomes:$\newline$$a_n = 27 + (n - 1) \times 2$
Simplify formula: Simplify the formula. $a_n = 27 + 2n - 2$ $a_n = 25 + 2n$