Question
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Answer
The first six terms of the sequence are 5, 4, 3, 2, 1, 0.
Solution
**Step 1:** Write down the general formula for the sequence:
\[
a_n = 6 - n
\]
**Step 2:** Find the first six terms by substituting \( n = 1, 2, 3, 4, 5, 6 \) into the formula.
- For \( n = 1 \):
\[
a_1 = 6 - 1 = 5
\]
- For \( n = 2 \):
\[
a_2 = 6 - 2 = 4
\]
- For \( n = 3 \):
\[
a_3 = 6 - 3 = 3
\]
- For \( n = 4 \):
\[
a_4 = 6 - 4 = 2
\]
- For \( n = 5 \):
\[
a_5 = 6 - 5 = 1
\]
- For \( n = 6 \):
\[
a_6 = 6 - 6 = 0
\]
**Final Answer:** The first six terms of the sequence are:
\[
5, \; 4, \; 3, \; 2, \; 1, \; 0
\]
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Simplify this solution Beyond the Answer
To find the first six terms of the sequence defined by \( a_{n} = 6 - n \), we simply plug in the values of \( n \) from 1 to 6. 1. For \( n = 1 \): \( a_1 = 6 - 1 = 5 \) 2. For \( n = 2 \): \( a_2 = 6 - 2 = 4 \) 3. For \( n = 3 \): \( a_3 = 6 - 3 = 3 \) 4. For \( n = 4 \): \( a_4 = 6 - 4 = 2 \) 5. For \( n = 5 \): \( a_5 = 6 - 5 = 1 \) 6. For \( n = 6 \): \( a_6 = 6 - 6 = 0 \) So, the first six terms are: \( 5, 4, 3, 2, 1, 0 \).
