Question

Find the first term of the arithmetic sequence in which a subscript 38 baseline equals negative 5 and the common difference is negative 2.9.
(1 point)
Responses

102.3
102.3

14.8
14.8

negative 105.8
Image with alt text: negative 105.8

negative 102.3

Answer 1

In an arithmetic sequence, the \( n \)-th term can be expressed using the formula:

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

where \( a_n \) is the \( n \)-th term, \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Given:
- \( a_{38} = -5 \)
- \( d = -2.9 \)
- \( n = 38 \)

We can plug these values into the formula to find \( a_1 \):

\[
-5 = a_1 + (38 - 1)(-2.9)
\]

This simplifies to:

\[
-5 = a_1 + 37(-2.9)
\]
\[
-5 = a_1 - 107.3
\]

Now, solving for \( a_1 \):

\[
a_1 = -5 + 107.3
\]
\[
a_1 = 102.3
\]

Thus, the first term of the arithmetic sequence is:

\[
\boxed{102.3}
\]