Complete the recursive formula of the geometric sequence {:[-0.25","-2","-16","-128","dots.],[b(1)=],[b(n)=b(n-1).]:}

Given Sequence: We are given the geometric sequence: -0.25, -2, -16, -128, ... To find the recursive formula, we need to determine the common ratio (r) by dividing any term by its preceding term. Let's divide the second term by the first term: r = (-2) / (-0.25) = 8.Common Ratio: Now that we have the common ratio, we can write the recursive formula. The first term b(1) is given as -0.25. The recursive formula will relate term b(n) to the previous term b(n-1) using the common ratio. The recursive formula is: b(n) = b(n-1) * r, where r = 8.Recursive Formula: Let's verify the recursive formula by applying it to find the third term using the second term. According to the formula, b(3) should equal b(2) * r. We have b(2) = -2 and r = 8, so b(3) = -2 * 8 = -16, which matches the given sequence.

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Complete the recursive formula of the geometric sequence

{:[-0.25","-2","-16","-128","dots.],[b(1)=],[b(n)=b(n-1).]:}

Complete the recursive formula of the geometric sequence $\newline$ $\begin{array}{l} -0.25,-2,-16,-128, \ldots . \\ b(1)=\square \\ b(n)=b(n-1) \cdot \square \end{array}$

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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} -0.25,-2,-16,-128, \ldots . \\ b(1)=\square \\ b(n)=b(n-1) \cdot \square \end{array}

Given Sequence: We are given the geometric sequence: $-0.25, -2, -16, -128, \ldots$ To find the recursive formula, we need to determine the common ratio $r$ by dividing any term by its preceding term. Let's divide the second term by the first term: $r = (-2) / (-0.25) = 8$ .
Common Ratio: Now that we have the common ratio, we can write the recursive formula. The first term $b(1)$ is given as $-0.25$ . The recursive formula will relate term $b(n)$ to the previous term $b(n-1)$ using the common ratio. $\newline$ The recursive formula is: $b(n) = b(n-1) \times r$ , where $r = 8$ .
Recursive Formula: Let's verify the recursive formula by applying it to find the third term using the second term. $\newline$ According to the formula, $b(3)$ should equal $b(2) \times r$ . $\newline$ We have $b(2) = -2$ and $r = 8$ , so $b(3) = -2 \times 8 = -16$ , which matches the given sequence.