Question

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

208,204,200,...

Find the 45th term.

(1 point)
a45=

Answer 1

To find the 45th term of the sequence given by the first three terms: 208, 204, 200, we first need to determine the pattern or rule of the sequence.

Let's look at the differences between the terms:

- The difference between the 1st term (208) and the 2nd term (204) is:
\[
204 - 208 = -4
\]

- The difference between the 2nd term (204) and the 3rd term (200) is:
\[
200 - 204 = -4
\]

The difference is consistent at -4, which indicates that this is an arithmetic sequence where each term decreases by 4. The first term \( a_1 = 208 \) and the common difference \( d = -4 \).

The formula for the \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]

Now we can substitute in the values to find the 45th term \( a_{45} \):
\[
a_{45} = 208 + (45 - 1) \cdot (-4)
\]

Calculating \( (45 - 1) \):
\[
a_{45} = 208 + 44 \cdot (-4)
\]
\[
a_{45} = 208 - 176
\]
\[
a_{45} = 32
\]

Thus, the 45th term of the sequence is:
\[
\boxed{32}
\]