Complete the recursive formula of the geometric sequence {:[-0.1","-0.5","-2.5","-12.5","dots.],[c(1)=],[c(n)=c(n-1).]:}

Find Common Ratio: We are given the sequence: -0.1, -0.5, -2.5, -12.5, ... To find the recursive formula, we need to determine the common ratio (r) by dividing any term by the previous term. Let's divide the second term by the first term to find r. r = (-0.5) / (-0.1) = 5Write Recursive Formula: Now that we have the common ratio, we can write the recursive formula. The recursive formula for a geometric sequence is given by: c(n) = c(n-1) * r We already know that r = 5, so we can substitute this value into the formula. c(n) = c(n-1) * 5Provide First Term: We also need to provide the first term of the sequence for the recursive formula to be complete. The first term, c(1), is given as -0.1. So, the recursive formula is: c(1) = -0.1 c(n) = c(n-1) * 5 for n > 1

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Complete the recursive formula of the geometric sequence

{:[-0.1","-0.5","-2.5","-12.5","dots.],[c(1)=],[c(n)=c(n-1).]:}

Complete the recursive formula of the geometric sequence $\newline$ $\begin{array}{l} -0.1,-0.5,-2.5,-12.5, \ldots . \\ c(1)=\square \\ c(n)=c(n-1) \cdot \square \end{array}$

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Algebra 1

Write variable expressions for geometric sequences

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Q. Complete the recursive formula of the geometric sequence

\newline

\begin{array}{l} -0.1,-0.5,-2.5,-12.5, \ldots . \\ c(1)=\square \\ c(n)=c(n-1) \cdot \square \end{array}

Find Common Ratio: We are given the sequence: $-0.1, -0.5, -2.5, -12.5, \ldots$ $\newline$ To find the recursive formula, we need to determine the common ratio $(r)$ by dividing any term by the previous term. $\newline$ Let's divide the second term by the first term to find $r$ . $\newline$ $r = \frac{-0.5}{-0.1} = 5$
Write Recursive Formula: Now that we have the common ratio, we can write the recursive formula. $\newline$ The recursive formula for a geometric sequence is given by: $\newline$ $c(n) = c(n-1) \times r$ $\newline$ We already know that $r = 5$ , so we can substitute this value into the formula. $\newline$ $c(n) = c(n-1) \times 5$
Provide First Term: We also need to provide the first term of the sequence for the recursive formula to be complete. $\newline$ The first term, $c(1)$ , is given as $-0.1$ . $\newline$ So, the recursive formula is: $\newline$ $c(1) = -0.1$ $\newline$ $c(n) = c(n-1) \times 5$ for n > 1