Questions: Write the first five terms of the sequence whose general term, (an), is given as (an=6 n-1).

Write the first five terms of the sequence whose general term, (an), is given as (an=6 n-1).
Transcript text: Write the first five terms of the sequence whose general term, $a_{n}$, is given as \[ \begin{array}{l} \text { Write the first five terms of the sequence whose } \\ \text { general term, } a_{n} \text {, is given as } \\ a_{n}=6 n-1 \end{array} \]
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Solution

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Solution Steps

To find the first five terms of the sequence, we need to substitute the values \( n = 1, 2, 3, 4, \) and \( 5 \) into the general term formula \( a_n = 6n - 1 \). This will give us the first five terms of the sequence.

Step 1: Identify the General Term

The general term of the sequence is given by \( a_n = 6n - 1 \).

Step 2: Substitute Values to Find Terms

To find the first five terms, substitute \( n = 1, 2, 3, 4, \) and \( 5 \) into the general term formula:

  • For \( n = 1 \): \[ a_1 = 6 \times 1 - 1 = 5 \]

  • For \( n = 2 \): \[ a_2 = 6 \times 2 - 1 = 11 \]

  • For \( n = 3 \): \[ a_3 = 6 \times 3 - 1 = 17 \]

  • For \( n = 4 \): \[ a_4 = 6 \times 4 - 1 = 23 \]

  • For \( n = 5 \): \[ a_5 = 6 \times 5 - 1 = 29 \]

Final Answer

The first five terms of the sequence are \(\boxed{5, 11, 17, 23, 29}\).

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