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

Identify Type: Identify whether the given sequence is geometric or arithmetic. The sequence -2, -14, -26, -38, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, d(n) = d(1) + (n-1)d, where d(1) is the first term and d is the common difference. For the sequence -2, -14, -26, -38, ..., the first term, d(1), is -2 and we need to find the common difference, d.Calculate Common Difference: Calculate the common difference, d, by subtracting the first term from the second term: d = -14 - (-2) = -14 + 2 = -12.Substitute Values: Substitute the values of d(1) and d into the formula to write an explicit formula for the sequence. The expression for the sequence -2, -14, -26, -38, ... is d(n) = -2 + (n-1)(-12).Simplify Expression: Simplify the expression to get the final explicit formula for the sequence. The simplified expression is d(n) = -2 - 12(n-1) = -2 - 12n + 12 = -12n + 10.

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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

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

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Note: the first term should be

d(1)

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d(n) = $\square$

Identify Type: Identify whether the given sequence is geometric or arithmetic. The sequence $-2, -14, -26, -38, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Use Explicit Formula: Use the explicit formula for an arithmetic sequence, $d(n) = d(1) + (n-1)d$ , where $d(1)$ is the first term and $d$ is the common difference. For the sequence $-2, -14, -26, -38, \ldots$ , the first term, $d(1)$ , is $-2$ and we need to find the common difference, $d$ .
Calculate Common Difference: Calculate the common difference, $d$ , by subtracting the first term from the second term: $d = -14 - (-2) = -14 + 2 = -12$ .
Substitute Values: Substitute the values of $d(1)$ and $d$ into the formula to write an explicit formula for the sequence. The expression for the sequence $-2, -14, -26, -38, \ldots$ is $d(n) = -2 + (n-1)(-12)$ .
Simplify Expression: Simplify the expression to get the final explicit formula for the sequence. The simplified expression is $d(n) = -2 - 12(n-1) = -2 - 12n + 12 = -12n + 10$ .