Question

Find a33 if the first term in the sequence is 3 and the common difference is -1.

A.
-29

B.
36

C.
-36

D.
-30

Answer 1

To find the \(33^{rd}\) term of an arithmetic sequence, we can use the formula for the \(n^{th}\) term of an arithmetic sequence:

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

where:
- \(a_n\) is the \(n^{th}\) term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

In this case:
- \(a_1 = 3\),
- \(d = -1\),
- \(n = 33\).

Plugging in these values:

\[
a_{33} = 3 + (33 - 1) \cdot (-1)
\]

\[
= 3 + 32 \cdot (-1)
\]

\[
= 3 - 32
\]

\[
= -29
\]

Therefore, the value of \(a_{33}\) is \(-29\).

So the answer is **A. -29**.