Find an explicit formula for the arithmetic sequence -5,13,31,49,dots. Note: the first term should be b(1). b(n)=

Identify Type: Identify whether the given sequence is geometric or arithmetic. The sequence -5, 13, 31, 49, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Find Common Difference: Determine the common difference, d, by subtracting the first term from the second term: d = 13 - (-5) = 18.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, b(n) = b(1) + (n-1)d, where b(1) is the first term and d is the common difference. For the sequence -5, 13, 31, 49, ..., the first term, b(1), is -5 and the common difference, d, is 18.Substitute Values: Substitute the values of b(1) and d into the formula to write an expression to describe the sequence. The expression for the sequence is b(n) = -5 + (n-1) × 18.Simplify Expression: Simplify the expression to get the final explicit formula for the sequence. b(n) = -5 + 18n - 18, which simplifies to b(n) = 18n - 23.

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Find an explicit formula for the arithmetic sequence
-5,13,31,49,dots. Note: the first term should be
b(1).

b(n)=

Find an explicit formula for the arithmetic sequence $\newline$ $-5,13,31,49, \ldots.$ $\newline$ Note: the first term should be $b(1)$ . $\newline$ b(n) = $\square$

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Algebra 2

Write a formula for an arithmetic sequence

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Q. Find an explicit formula for the arithmetic sequence

\newline

-5,13,31,49, \ldots.

\newline

Note: the first term should be

b(1)

\newline

b(n) = $\square$

Identify Type: Identify whether the given sequence is geometric or arithmetic. The sequence $-5, 13, 31, 49, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Find Common Difference: Determine the common difference, $d$ , by subtracting the first term from the second term: $d = 13 - (-5) = 18$ .
Use Explicit Formula: Use the explicit formula for an arithmetic sequence, $b(n) = b(1) + (n-1)d$ , where $b(1)$ is the first term and $d$ is the common difference. For the sequence $-5, 13, 31, 49, \ldots$ , the first term, $b(1)$ , is $-5$ and the common difference, $d$ , is $18$ .
Substitute Values: Substitute the values of $b(1)$ and $d$ into the formula to write an expression to describe the sequence. The expression for the sequence is $b(n) = -5 + (n-1) \times 18$ .
Simplify Expression: Simplify the expression to get the final explicit formula for the sequence. $b(n) = -5 + 18n - 18$ , which simplifies to $b(n) = 18n - 23$ .