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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
7,15,23,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $7,15,23, \ldots$ $\newline$ Answer: $a_{n}=$

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Write a formula for an arithmetic sequence

Full solution

Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

7,15,23, \ldots

\newline

Answer:

a_{n}=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $7, 15, 23, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Find First Term and Difference: Determine the first term ( $a_1$ ) and the common difference ( $d$ ) of the sequence. The first term $a_1$ is $7$ . To find the common difference, subtract the first term from the second term: $d = 15 - 7 = 8$ .
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 $7, 15, 23, \ldots$ , $a_1$ is $7$ and $d$ is $8$ .
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 $7, 15, 23, \ldots$ is $a_n = 7 + (n-1) \times 8$ .
Simplify Expression: Simplify the expression to find the explicit formula for the nth term. $a_n = 7 + 8n - 8$ , which simplifies to $a_n = 8n - 1$ .

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