Find an explicit formula for the arithmetic sequence -2,-14,-26,-38,dots.. Note: the first term should be d(1). d(n)=

Identify the sequence type and pattern: Identify the type of sequence and the pattern. The sequence -2, -14, -26, -38, ... decreases by the same amount each time, which indicates it is an arithmetic sequence. The common difference (d) can be found by subtracting any term from the term that follows it. Calculation: d = -14 - (-2) = -14 + 2 = -12Calculate the common difference: Use the explicit formula for an arithmetic sequence, which is d(n) = d(1) + (n-1)d, where d(1) is the first term and d is the common difference. In this sequence, the first term d(1) is -2 and the common difference d is -12.Use the explicit formula for arithmetic sequence: Substitute the values of d(1) and d into the formula to find the explicit formula for the sequence. Calculation: d(n) = -2 + (n-1)(-12)Substitute values into the formula: Simplify the expression to get the final explicit formula for the sequence. Calculation: d(n) = -2 - 12(n-1) = -2 - 12n + 12 = -12n + 10

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Find an explicit formula for the arithmetic sequence
-2,-14,-26,-38,dots.. Note: the first term should be
d(1).

d(n)=

Find an explicit formula for the arithmetic sequence $\newline$ $-2,-14,-26,-38, \ldots \text {.. }$ $\newline$ Note: the first term should be $d(1)$ . $\newline$ $d(n)=$

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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

\newline

-2,-14,-26,-38, \ldots \text {.. }

\newline

Note: the first term should be

d(1)

\newline

d(n)=

Identify the sequence type and pattern: Identify the type of sequence and the pattern. The sequence -2 ext{,} -14 ext{,} -26 ext{,} -38 ext{,} \ ext{...} ext{)} decreases by the same amount each time, which indicates it is an arithmetic sequence. The common difference \$d can be found by subtracting any term from the term that follows it. $\newline$ Calculation: $d = -14 - (-2) = -14 + 2 = -12$
Calculate the common difference: Use the explicit formula for an arithmetic sequence, which is $d(n) = d(1) + (n-1)d$ , where $d(1)$ is the first term and $d$ is the common difference. $\newline$ In this sequence, the first term $d(1)$ is $-2$ and the common difference $d$ is $-12$ .
Use the explicit formula for arithmetic sequence: Substitute the values of $d(1)$ and $d$ into the formula to find the explicit formula for the sequence. $\newline$ Calculation: $d(n) = -2 + (n-1)(-12)$
Substitute values into the formula: Simplify the expression to get the final explicit formula for the sequence. $\newline$ Calculation: $d(n) = -2 - 12(n-1) = -2 - 12n + 12 = -12n + 10$