Complete the recursive formula of the arithmetic sequence {:[-16","-33","-50","-67","dots],[c(1)=],[c(n)=c(n-1)+◻]:}

Identify the pattern: Identify the pattern in the sequence to determine the common difference. The sequence is -16, -33, -50, -67, .... To find the common difference, subtract the first term from the second term: -33 - (-16) = -33 + 16 = -17.Verify the common difference: Verify the common difference by subtracting the second term from the third term: -50 - (-33) = -50 + 33 = -17. The common difference is consistent, confirming that the sequence is arithmetic with a common difference of -17.Write the recursive formula: Write the recursive formula for the arithmetic sequence. The recursive formula has the form c(n) = c(n-1) + d, where d is the common difference. Since we have determined that the common difference is -17, the recursive formula is c(n) = c(n-1) - 17.State the initial term: State the initial term of the sequence in the recursive formula. The first term, c(1), is given as -16. Therefore, the complete recursive formula is: c(1) = -16, c(n) = c(n-1) - 17 for n > 1.

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Complete the recursive formula of the arithmetic sequence

{:[-16","-33","-50","-67","dots],[c(1)=],[c(n)=c(n-1)+◻]:}

Complete the recursive formula of the arithmetic sequence $\newline$ $\begin{array}{l} -16,-33,-50,-67, \ldots . \\ c(1)= \\ c(n)=c(n-1)+\square \end{array}$

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Algebra 2

Write a formula for an arithmetic sequence

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Q. Complete the recursive formula of the arithmetic sequence

\newline

\begin{array}{l} -16,-33,-50,-67, \ldots . \\ c(1)= \\ c(n)=c(n-1)+\square \end{array}

Identify the pattern: Identify the pattern in the sequence to determine the common difference. The sequence is $-16$ , $-33$ , $-50$ , $-67$ , .... To find the common difference, subtract the first term from the second term: $-33 - (-16) = -33 + 16 = -17$ .
Verify the common difference: Verify the common difference by subtracting the second term from the third term: $-50 - (-33) = -50 + 33 = -17$ . The common difference is consistent, confirming that the sequence is arithmetic with a common difference of $-17$ .
Write the recursive formula: Write the recursive formula for the arithmetic sequence. The recursive formula has the form $c(n) = c(n-1) + d$ , where $d$ is the common difference. Since we have determined that the common difference is $-17$ , the recursive formula is $c(n) = c(n-1) - 17$ .
State the initial term: State the initial term of the sequence in the recursive formula. The first term, $c(1)$ , is given as $-16$ . Therefore, the complete recursive formula is: $\newline$ $c(1) = -16,$ $\newline$ c(n) = c(n-1) - 17 \text{ for } n > 1.