Using d = 2, what is the 5th term of the arithmetic sequence starting at 1?

To determine the 5th term of an arithmetic sequence where the first term is 1 and the common difference ( d ) is 2, you can use the formula for the ( n )-th term of an arithmetic sequence:

[

a_n = a_1 + (n - 1) \cdot d

]

In this situation, ( a_1 ) is the first term (1), ( d ) is the common difference (2), and ( n ) is the term number you want to find, which is 5.

Substituting the values into the formula:

[

a_5 = 1 + (5 - 1) \cdot 2

]

Calculating the expression step-by-step:

1. ( 5 - 1 = 4 )

2. ( 4 \cdot 2 = 8 )

3. Adding this to the first term gives ( 1 + 8 = 9 )

Now, it becomes clear that the 5th term evaluates to 9, showing that the correct answer is indeed 9.