Questions: 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
\[
\begin{array}{l}
\text { Write the first five terms of the sequence whose } \\
\text { general term, } a_{n} \text {, is given as } \\
a_{n}=6 n-1
\end{array}
\]
Solution
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 \(\boxed{5, 11, 17, 23, 29}\).