Find an explicit formula for the arithmetic sequence -11,-3,5,13,dots Note: the first term should be b(1). b(n) = ◻

Identify Sequence Type: Identify the type of sequence. The sequence -11, -3, 5, 13, ... has a common difference between consecutive terms, indicating that it is an arithmetic sequence.Calculate Common Difference: Calculate the common difference (d) of the sequence. To find the common difference, subtract the first term from the second term: d = -3 - (-11) = -3 + 11 = 8.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, which is b(n) = b(1) + (n-1)d, where b(1) is the first term and d is the common difference. For this sequence, the first term, b(1), is -11 and the common difference, d, is 8.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) = -11 + (n-1) × 8.Simplify Expression: Simplify the expression. b(n) = -11 + 8n - 8, which simplifies to b(n) = 8n - 19.

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Find an explicit formula for the arithmetic sequence -11,-3,5,13,dots
Note: the first term should be b(1).
b(n) = ◻

Find an explicit formula for the arithmetic sequence $-11,-3,5,13, \ldots$ $\newline$ 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

-11,-3,5,13, \ldots

\newline

Note: the first term should be

b(1)

\newline

b(n) = \square

Identify Sequence Type: Identify the type of sequence. The sequence $-11, -3, 5, 13, \ldots$ has a common difference between consecutive terms, indicating that it is an arithmetic sequence.
Calculate Common Difference: Calculate the common difference $d$ of the sequence. To find the common difference, subtract the first term from the second term: $d = -3 - (-11) = -3 + 11 = 8$ .
Use Explicit Formula: Use the explicit formula for an arithmetic sequence, which is $b(n) = b(1) + (n-1)d$ , where $b(1)$ is the first term and $d$ is the common difference. For this sequence, the first term, $b(1)$ , is $-11$ and the common difference, $d$ , is $8$ .
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 $b(n) = -11 + (n-1) \times 8$ .
Simplify Expression: Simplify the expression. $b(n) = -11 + 8n - 8$ , which simplifies to $b(n) = 8n - 19$ .