Write an explicit formula for a_(n), the n^("th ") term of the sequence 20,23,26,dots Answer: a_(n)=

Identify Pattern: Identify the pattern in the sequence. The sequence starts at 20 and each term increases by 3. This is an arithmetic sequence with a common difference (d) of 3.Determine First Term: Determine the first term (a_1) of the sequence. The first term of the sequence is given as 20.Use Formula: Use the formula for the nth term of an arithmetic sequence. The formula for the nth term (a_n) of an arithmetic sequence is a_n = a_1 + (n - 1)d.Substitute Values: Substitute the values of a_1 and d into the formula. a_1 = 20 and d = 3, so a_n = 20 + (n - 1) * 3.Simplify Formula: Simplify the formula. a_n = 20 + 3n - 3 a_n = 3n + 17

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
20,23,26,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $20,23,26, \ldots$ $\newline$ 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

20,23,26, \ldots

\newline

Answer:

a_{n}=

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence starts at $20$ and each term increases by $3$ . This is an arithmetic sequence with a common difference $(d)$ of $3$ .
Determine First Term: Determine the first term $a_1$ of the sequence. $\newline$ The first term of the sequence is given as $20$ .
Use Formula: Use the formula for the $n$ th term of an arithmetic sequence. $\newline$ The formula for the $n$ th term ( $a_n$ ) of an arithmetic sequence is $a_n = a_1 + (n - 1)d$ .
Substitute Values: Substitute the values of $a_1$ and $d$ into the formula. $\newline$ $a_1 = 20$ and $d = 3$ , so $a_n = 20 + (n - 1) \times 3$ .
Simplify Formula: Simplify the formula. $\newline$ $a_n = 20 + 3n - 3$ $\newline$ $a_n = 3n + 17$