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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
17,27,37,dots.
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $17,27,37, \ldots$ . $\newline$ Answer: $a_{n}=$

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Evaluate an exponential function

Full solution

Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

17,27,37, \ldots

.

\newline

Answer:

a_{n}=

Calculate 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. We can do this by subtracting the first term from the second term. $\newline$ Calculation: $27 - 17 = 10$
Find nth Term Formula: The common difference is $10$ . This means that each term is $10$ more than the previous term. Since the first term is $17$ , the nth term can be found by starting with $17$ and adding the common difference ( $10$ ) multiplied by $(n - 1)$ times. $\newline$ Calculation: $a_n = 17 + 10(n - 1)$
Simplify nth Term Formula: Now we simplify the formula for the nth term. $\newline$ Calculation: $a_n = 17 + 10n - 10$ $\newline$ Calculation: $a_n = 10n + 7$

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