Question

18.
Find the value of the term in the arithmetic sequence
-4,0,4,8,12. . .(9th term)
A. a 9=32
B. a 9=28
C.a 9=20
D.a 9=18

Answer 1

In an arithmetic sequence, the nth term can be found using the formula:

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

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

In this sequence:
- The first term \(a_1 = -4\).
- The common difference \(d\) can be calculated as follows:
\[
d = 0 - (-4) = 4
\]
(This is consistent since \(4 - 0 = 4\), \(8 - 4 = 4\), etc.)

Now we can calculate the 9th term using the formula:

\[
a_9 = a_1 + (9 - 1) \cdot d
\]
\[
a_9 = -4 + 8 \cdot 4
\]
\[
a_9 = -4 + 32
\]
\[
a_9 = 28
\]

Thus, the 9th term \(a_9\) is \(28\).

The answer is **B. \(a_9 = 28\)**.