Question

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

Answer 1

In an arithmetic sequence, the difference between consecutive terms is constant.

To find the common difference (\(d\)), we can subtract the first term from the second term:

\[
d = 5 - 9 = -4
\]

We can also verify this with the next terms:

\[
1 - 5 = -4
\]
\[
-3 - 1 = -4
\]

Now that we have the common difference \(d = -4\), we can find the \(n\)-th term of the sequence using the formula:

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

where \(a_1\) is the first term, and \(n\) is the term number. In this case, \(a_1 = 9\).

To find the 6th term (\(a_6\)):

\[
a_6 = a_1 + (6-1) \cdot d
\]
\[
a_6 = 9 + (5) \cdot (-4)
\]
\[
a_6 = 9 - 20
\]
\[
a_6 = -11
\]

So, the \(6\)th term \(a_6\) is \(\boxed{-11}\).