Question

In the first term in an arithmetic sequence is 4 and the second term is (-6), which of the following is the third term? (1 point)
Responses

-10
-10

4
4

10
10

-16

Answer 1

An arithmetic sequence has a common difference between consecutive terms.

Given:
- First term (\( a_1 \)) = 4
- Second term (\( a_2 \)) = -6

The common difference (\( d \)) can be calculated as:
\[
d = a_2 - a_1 = -6 - 4 = -10
\]

To find the third term (\( a_3 \)), we can use the formula:
\[
a_3 = a_2 + d
\]

Substituting the known values:
\[
a_3 = -6 + (-10) = -6 - 10 = -16
\]

Thus, the third term in the sequence is \(-16\).

The correct response is:
-16