Write an explicit formula for a_(n), the n^("th ") term of the sequence 9,14,19,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.Calculate Common Difference: We subtract the first term from the second term to find the common difference. 14 - 9 = 5Identify Arithmetic Sequence: The common difference is 5. This means that each term is 5 more than the previous term. The sequence is an arithmetic sequence.Arithmetic Sequence Formula: The explicit formula 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: We know that a_1 = 9 and d = 5. Let's substitute these values into the formula. a_n = 9 + (n - 1) * 5Distribute and Simplify: Simplify the formula by distributing the 5 into the parentheses. a_n = 9 + 5n - 5Combine Like Terms: Combine like terms to get the final explicit formula. a_n = 5n + 4

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
9,14,19,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $9,14,19, \ldots$ $\newline$ Answer: $a_{n}=$

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Math Problems

Algebra 1

Evaluate variable expressions for number sequences

Full solution

Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

9,14,19, \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.
Calculate Common Difference: We subtract the first term from the second term to find the common difference. $14 - 9 = 5$
Identify Arithmetic Sequence: The common difference is $5$ . This means that each term is $5$ more than the previous term. The sequence is an arithmetic sequence.
Arithmetic Sequence Formula: The explicit formula 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: We know that $a_1 = 9$ and $d = 5$ . Let's substitute these values into the formula. $\newline$ $a_n = 9 + (n - 1) \times 5$
Distribute and Simplify: Simplify the formula by distributing the $5$ into the parentheses. $a_n = 9 + 5n - 5$
Combine Like Terms: Combine like terms to get the final explicit formula. $a_n = 5n + 4$