Question

find the first 5 terms.\

$$\begin{cases}a_0 = 100\\\\a_n = a_{n - 1}-7\\end{cases}$$

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$$\begin{tabular}{|c|c|c|c|c|}\\hline$a_0$&$a_1$&$a_2$&$a_3$&$a_4$\\\\\\hline?&\\ \\ &\\ \\ &\\ \\ &\\ \\ \\\\\\hline\\end{tabular}$$

Explanation:

Step1: Identify the initial term

We know that \( a_0 = 100 \).

Step2: Calculate \( a_1 \)

Using the recurrence relation \( a_n=a_{n - 1}-7 \), for \( n = 1 \), we have \( a_1=a_{0}-7 \). Substituting \( a_0 = 100 \), we get \( a_1=100 - 7=93 \).

Step3: Calculate \( a_2 \)

For \( n = 2 \), \( a_2=a_{1}-7 \). Substituting \( a_1 = 93 \), we get \( a_2=93 - 7 = 86 \).

Step4: Calculate \( a_3 \)

For \( n=3 \), \( a_3=a_{2}-7 \). Substituting \( a_2 = 86 \), we get \( a_3=86 - 7=79 \).

Step5: Calculate \( a_4 \)

For \( n = 4 \), \( a_4=a_{3}-7 \). Substituting \( a_3 = 79 \), we get \( a_4=79 - 7 = 72 \).

Answer:

\( a_0 = 100 \), \( a_1=93 \), \( a_2 = 86 \), \( a_3=79 \), \( a_4 = 72 \)