Find an explicit formula for the arithmetic sequence -31,-27,-23,-19,dots. Note: the first term should be b(1). b(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence -31, -27, -23, -19, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, bn = b1 + (n-1)d, where b1 is the first term and d is the common difference. For the sequence -31, -27, -23, -19, ..., the first term, b1, is -31 and the common difference, d, is 4 (since -27 - (-31) = 4).Substitute Values: Substitute the values of b1 and d into the formula to write an explicit formula for the sequence. The expression for the sequence -31, -27, -23, -19, ... is bn = -31 + (n-1) × 4.Simplify Expression: Simplify the expression to find the final explicit formula. bn = -31 + 4n - 4, which simplifies to bn = 4n - 35.

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Find an explicit formula for the arithmetic sequence
-31,-27,-23,-19,dots.
Note: the first term should be
b(1).

b(n)=

Find an explicit formula for the arithmetic sequence $-31,-27,-23,-19, \ldots$ .. $\newline$ Note: the first term should be $b(1)$ . $\newline$ $b(n)=$

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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

-31,-27,-23,-19, \ldots

\newline

Note: the first term should be

b(1)

\newline

b(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $-31$ , $-27$ , $-23$ , $-19$ , ... has a common difference between consecutive terms, so it is an arithmetic sequence.
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 $-31, -27, -23, -19, \ldots$ , the first term, $b_1$ , is $-31$ and the common difference, $d$ , is $4$ (since $-27 - (-31) = 4$ ).
Substitute Values: Substitute the values of $b_1$ and $d$ into the formula to write an explicit formula for the sequence. The expression for the sequence $-31, -27, -23, -19, \ldots$ is $b_n = -31 + (n-1) \times 4$ .
Simplify Expression: Simplify the expression to find the final explicit formula. $b_n = -31 + 4n - 4$ , which simplifies to $b_n = 4n - 35$ .