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

$\left\{\begin{array}{l} b(1)=-500 \\ b(n)=b(n-1) \cdot \frac{4}{5} \end{array}\right.$ $\newline$ What is the $3^{\text {rd }}$ term in the sequence? $\newline$ $\square$

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 $-320$ .