Question

name the first five terms of each arithmetic sequence descried.
a_(1) =38 d=-4

Answer 1

In an arithmetic sequence, the first term is denoted as \( a_1 \) and the common difference as \( d \). The general formula for the \( n \)-th term of an arithmetic sequence is given by:

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

Given:
- \( a_1 = 38 \)
- \( d = -4 \)

Now, we will calculate the first five terms:

1. \( a_1 = 38 \)
2. \( a_2 = a_1 + d = 38 + (-4) = 38 - 4 = 34 \)
3. \( a_3 = a_2 + d = 34 + (-4) = 34 - 4 = 30 \)
4. \( a_4 = a_3 + d = 30 + (-4) = 30 - 4 = 26 \)
5. \( a_5 = a_4 + d = 26 + (-4) = 26 - 4 = 22 \)

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

38, 34, 30, 26, 22.