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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) = \(\square\)

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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) = \(\square\)

Identify Type: Identify whether the given sequence is geometric or arithmetic. The sequence $-31, -27, -23, -19, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Use 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 expression to describe 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 explicit formula. $b_n = -31 + 4n - 4$ , which simplifies to $b_n = 4n - 35$ .

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