{[b(1)=-500],[b(n)=b(n-1)*(4)/(5)]:} What is the 3^("rd ") term in the sequence? ◻

Identify first term and formula: Identify the first term of the sequence and the recursive formula. The first term b(1) is given as -500. The recursive formula to find the nth term is b(n) = b(n-1) * (4/5), which means each term is 4/5 times the previous term.Find second term: Find the second term using the recursive formula. To find the second term b(2), we use the first term b(1) and multiply it by 4/5. b(2) = b(1) * (4/5) = -500 * (4/5)Calculate second term: Calculate the value of the second term. b(2) = -500 * (4/5) = -400 The second term in the sequence is -400.Find third term: Find the third term using the recursive formula. To find the third term b(3), we use the second term b(2) and multiply it by 4/5. b(3) = b(2) * (4/5) = -400 * (4/5)Calculate third term: Calculate the value of the third term. b(3) = -400 * (4/5) = -320 The third term in the sequence is -320.

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Calculus

Find higher derivatives of rational and radical functions

Full solution

\left\{\begin{array}{l} b(1)=-500 \\ b(n)=b(n-1) \cdot \frac{4}{5} \end{array}\right.

\newline

What is the

3^{\text {rd }}

term in the sequence?

\newline

\square

Identify first term and formula: Identify the first term of the sequence and the recursive formula. $\newline$ The first term $b(1)$ is given as $-500$ . The recursive formula to find the nth term is $b(n) = b(n-1) \times \left(\frac{4}{5}\right)$ , which means each term is $\frac{4}{5}$ times the previous term.
Find second term: Find the second term using the recursive formula. $\newline$ To find the second term $b(2)$ , we use the first term $b(1)$ and multiply it by $\frac{4}{5}$ . $\newline$ $b(2) = b(1) \times \left(\frac{4}{5}\right) = -500 \times \left(\frac{4}{5}\right)$
Calculate second term: Calculate the value of the second term. $b(2) = -500 \times \left(\frac{4}{5}\right) = -400$ The second term in the sequence is $-400$ .
Find third term: Find the third term using the recursive formula. $\newline$ To find the third term $b(3)$ , we use the second term $b(2)$ and multiply it by $\frac{4}{5}$ . $\newline$ $b(3) = b(2) \times \left(\frac{4}{5}\right) = -400 \times \left(\frac{4}{5}\right)$
Calculate third term: Calculate the value of the third term. $\newline$ $b(3) = -400 \times \left(\frac{4}{5}\right) = -320$ $\newline$ The third term in the sequence is $-320$ .