The $n$th term of an arithmetic sequence is given.
\[
a_{n}=3+2(n-1)
\]
(a) Find the first five terms of the sequence.
\[
\begin{array}{l}
a_{1}= \\
a_{2}= \\
a_{3}= \\
a_{4}= \\
a_{5}=
\end{array}
\]
(b) What is the common difference $d$ ?
\[
d=
\]
Answer
The first five terms of the sequence are \(\boxed{3, 5, 7, 9, 11}\) and the common difference \(d\) is \(\boxed{2}\)
Step 1 ：Substitute the values 1, 2, 3, 4, and 5 into the formula for \(a_n\) to find the first five terms of the sequence.
Step 2 ：\(a_1 = 3 + 2(1 - 1) = 3\)
Step 3 ：\(a_2 = 3 + 2(2 - 1) = 5\)
Step 4 ：\(a_3 = 3 + 2(3 - 1) = 7\)
Step 5 ：\(a_4 = 3 + 2(4 - 1) = 9\)
Step 6 ：\(a_5 = 3 + 2(5 - 1) = 11\)
Step 7 ：Subtract \(a_{n-1}\) from \(a_n\) to find the common difference \(d\).
Step 8 ：\(d = a_2 - a_1 = 5 - 3 = 2\)
Step 9 ：The first five terms of the sequence are \(\boxed{3, 5, 7, 9, 11}\) and the common difference \(d\) is \(\boxed{2}\)
