Question

Given the first four terms of the arithmetic sequence: 9, 5, 1, −3,...
find a6
:(1 point)
a6 =

Answer 1

To find the sixth term \( a_6 \) of the arithmetic sequence given, we first need to identify the common difference \( d \) of the sequence.

The first four terms are:
- \( a_1 = 9 \)
- \( a_2 = 5 \)
- \( a_3 = 1 \)
- \( a_4 = -3 \)

Now, we calculate the common difference \( d \):
\[
d = a_2 - a_1 = 5 - 9 = -4
\]
\[
d = a_3 - a_2 = 1 - 5 = -4
\]
\[
d = a_4 - a_3 = -3 - 1 = -4
\]

Since the common difference \( d \) is consistent at \( -4 \), we can use this to find the subsequent terms.

We can use the formula for the \( n \)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n - 1) d
\]

We need to find the sixth term \( a_6 \):
\[
a_6 = a_1 + (6 - 1) d = 9 + 5(-4)
\]
\[
a_6 = 9 + 5(-4) = 9 - 20 = -11
\]

Thus, the sixth term \( a_6 \) is:
\[
\boxed{-11}
\]