Question

find the first 5 terms.
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$$\begin{cases} a_0 = 6 \\\\ a_n = a_{n - 1} + 0.5 \\end{cases}$$

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

Explanation:

Step1: Identify the initial term

We know that \( a_0 = 6 \).

Step2: Find \( a_1 \)

Using the recurrence relation \( a_n = a_{n - 1}+0.5 \), for \( n = 1 \), we have \( a_1=a_0 + 0.5 \). Substituting \( a_0 = 6 \), we get \( a_1=6 + 0.5=6.5 \).

Step3: Find \( a_2 \)

For \( n = 2 \), \( a_2=a_1 + 0.5 \). Substituting \( a_1 = 6.5 \), we get \( a_2=6.5+0.5 = 7 \).

Step4: Find \( a_3 \)

For \( n = 3 \), \( a_3=a_2 + 0.5 \). Substituting \( a_2 = 7 \), we get \( a_3=7 + 0.5=7.5 \).

Step5: Find \( a_4 \)

For \( n = 4 \), \( a_4=a_3 + 0.5 \). Substituting \( a_3 = 7.5 \), we get \( a_4=7.5+0.5 = 8 \).

Answer:

\( a_0 = 6 \), \( a_1 = 6.5 \), \( a_2 = 7 \), \( a_3 = 7.5 \), \( a_4 = 8 \)