dictetzqh

2021-11-15

The analysis of accidents which happen per year is the average of the number of accidents which occurred in the 2 previous years
a) Calculate a recurrence relation for $\left\{{A}_{n}\right\}$ where ${A}_{n}$ is the number of accidents which happened in year x using the information given in the question above
b) Considering that three hundred thousand accidents occurred in year two and hundred thousand accidents occurred in year one, calculate the value for ${A}_{n}$

Alfonso Miller

Step 1
Part (a)
Let ${A}_{n}$ be the number of accidents happened in year x named as ${a}_{n}$ and are the number of accidents that happened in two preceding two years.
Then according to question,
${a}_{n}=\frac{{a}_{n-1}+{a}_{n-2}}{2}$
Therefore, the recurrence relation is ${a}_{n}=\frac{{a}_{n-1}+{a}_{n-2}}{2}$
Step 2
Part (b)
Substitute $300,00$ for ${a}_{n-1}$ and $100,000$ for ${a}_{n-2}$ in the equation
${a}_{n}=\frac{{a}_{n-1}+{a}_{n-2}}{2}$
to calculate the value of ${a}_{n}$
${a}_{n}=\frac{300,000+100,000}{2}$
$=200,000$
Therefore, the value of ${a}_{n}$ is 200,000

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