Question

name the first five terms of each arithmetic sequence descried.
a_(1) =4, d=3

Answer 1

To find the first five terms of the arithmetic sequence defined by \( a_1 = 4 \) (the first term) and \( d = 3 \) (the common difference), we can use the formula for the \( n \)-th term of an arithmetic sequence:

\[
a_n = a_1 + (n - 1) \times d
\]

Now, we can calculate the first five terms:

1. For \( n = 1 \):
\[
a_1 = 4
\]

2. For \( n = 2 \):
\[
a_2 = 4 + (2 - 1) \times 3 = 4 + 3 = 7
\]

3. For \( n = 3 \):
\[
a_3 = 4 + (3 - 1) \times 3 = 4 + 6 = 10
\]

4. For \( n = 4 \):
\[
a_4 = 4 + (4 - 1) \times 3 = 4 + 9 = 13
\]

5. For \( n = 5 \):
\[
a_5 = 4 + (5 - 1) \times 3 = 4 + 12 = 16
\]

Therefore, the first five terms of the arithmetic sequence are:

**4, 7, 10, 13, 16**.