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

Determine First Term: To find an explicit formula for an arithmetic sequence, we need to determine the first term (b(1)) and the common difference (d). The first term is given as -11.Calculate Common Difference: Next, we calculate the common difference (d) by subtracting the first term from the second term: d = -3 - (-11) = -3 + 11 = 8.Write Explicit Formula: Now that we have the first term (b(1) = -11) and the common difference (d = 8), we can write the explicit formula for the nth term of the arithmetic sequence as b(n) = b(1) + (n - 1)d.Substitute Values: Substitute the values of b(1) and d into the formula: b(n) = -11 + (n - 1)8.Simplify Formula: Simplify the formula to get the final explicit formula: b(n) = -11 + 8n - 8.Combine Like Terms: Combine like terms to get the simplified explicit formula: b(n) = 8n - 19.

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

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Q. Find an explicit formula for the arithmetic sequence

\newline

-11,-3,5,13,\dots

\newline

Note: the first term should be

b(1)

\newline

b(n)=\square

Determine First Term: To find an explicit formula for an arithmetic sequence, we need to determine the first term ( $b(1)$ ) and the common difference ( $d$ ). The first term is given as $-11$ .
Calculate Common Difference: Next, we calculate the common difference $d$ by subtracting the first term from the second term: $d = -3 - (-11) = -3 + 11 = 8$ .
Write Explicit Formula: Now that we have the first term $b(1) = -11$ and the common difference $d = 8$ , we can write the explicit formula for the $n$ th term of the arithmetic sequence as $b(n) = b(1) + (n - 1)d$ .
Substitute Values: Substitute the values of $b(1)$ and $d$ into the formula: $b(n) = -11 + (n - 1)8$ .
Simplify Formula: Simplify the formula to get the final explicit formula: $b(n) = -11 + 8n - 8$ .
Combine Like Terms: Combine like terms to get the simplified explicit formula: $b(n) = 8n - 19$ .