Find an explicit formula for the arithmetic sequence 10,-10,-30,-50,dots".. " Note: the first term should be c(1). c(n)=◻

Identify sequence type: Identify whether the given sequence is geometric or arithmetic. The sequence 10, -10, -30, -50, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Determine first term and common difference: Determine the first term (c(1)) and the common difference (d) of the sequence. The first term c(1) is 10. To find the common difference, subtract the second term from the first term: d = -10 - 10 = -20.Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, c(n) = c(1) + (n-1)d, where c(1) is the first term and d is the common difference. For this sequence, c(1) = 10 and d = -20.Write expression for the sequence: Substitute the values of c(1) and d into the formula to write an expression to describe the sequence. The expression for the sequence is c(n) = 10 + (n-1)(-20).Simplify the expression: Simplify the expression. c(n) = 10 - 20(n-1) = 10 - 20n + 20 = 30 - 20n.

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Find an explicit formula for the arithmetic sequence

10,-10,-30,-50,dots".. "
Note: the first term should be
c(1).

c(n)=◻

Find an explicit formula for the arithmetic sequence $\newline$ $10,-10,-30,-50, \ldots \text {.. }$ $\newline$ Note: the first term should be $c(1)$ . $\newline$ $c(n)=\square$

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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

10,-10,-30,-50, \ldots \text {.. }

\newline

Note: the first term should be

c(1)

\newline

c(n)=\square

Identify sequence type: Identify whether the given sequence is geometric or arithmetic. The sequence $10, -10, -30, -50, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Determine first term and common difference: Determine the first term $c(1)$ and the common difference $d$ of the sequence. The first term $c(1)$ is $10$ . To find the common difference, subtract the second term from the first term: $d = -10 - 10 = -20$ .
Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, $c(n) = c(1) + (n-1)d$ , where $c(1)$ is the first term and $d$ is the common difference. For this sequence, $c(1) = 10$ and $d = -20$ .
Write expression for the sequence: Substitute the values of $c(1)$ and $d$ into the formula to write an expression to describe the sequence. The expression for the sequence is $c(n) = 10 + (n-1)(-20)$ .
Simplify the expression: Simplify the expression. $c(n) = 10 - 20(n-1) = 10 - 20n + 20 = 30 - 20n$ .