Question2) If $b_{0}=1.4, b_{1}=8$ and $b_{m}=\frac{3-b_{m-2}}{b_{m-1}}$ , then $b_{3}=$ (A) -25 (B) -3.57 (C) 0.20 (D) 0.82 (E) 1.40

Studdy Solution

STEP 1

1. The sequence $b_m$ is defined recursively.
2. We are given initial values $b_0 = 1.4$ and $b_1 = 8$ .
3. We need to compute $b_2$ and $b_3$ using the recursive formula $b_m = \frac{3 - b_{m-2}}{b_{m-1}}$ .

STEP 2

1. Calculate $b_2$ using the recursive formula.
2. Calculate $b_3$ using the recursive formula.
3. Determine which option matches $b_3$ .

STEP 3

Use the recursive formula to calculate $b_2$ :
$b_2 = \frac{3 - b_0}{b_1}$
Substitute the known values $b_0 = 1.4$ and $b_1 = 8$ :
$b_2 = \frac{3 - 1.4}{8}$ $b_2 = \frac{1.6}{8}$ $b_2 = 0.2$

STEP 4

Use the recursive formula to calculate $b_3$ :
$b_3 = \frac{3 - b_1}{b_2}$
Substitute the known values $b_1 = 8$ and $b_2 = 0.2$ :
$b_3 = \frac{3 - 8}{0.2}$ $b_3 = \frac{-5}{0.2}$ $b_3 = -25$

STEP 5

Compare the calculated value of $b_3$ with the given options:
The value of $b_3$ is:
$\boxed{-25}$
This matches option (A).

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