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).
203, comma, 199, comma, 195, comma, point, point, .
203,199,195,...
Find the 35th term.
Find the 35th term.

Answer 1

To find the pattern in the sequence \( 203, 199, 195, \ldots \), we first calculate the differences between the consecutive terms:

\[
199 - 203 = -4
\]
\[
195 - 199 = -4
\]

The sequence shows a consistent decrease by 4. Therefore, we can describe the \( n \)-th term of the sequence with the following formula:

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

where:
- \( a_1 = 203 \) (the first term),
- \( d = -4 \) (the common difference).

We want to find the 35th term, \( a_{35} \):

\[
a_{35} = a_1 + (35 - 1) \cdot (-4)
\]

Now, substituting the known values:

\[
a_{35} = 203 + (34) \cdot (-4)
\]
\[
a_{35} = 203 - 136
\]
\[
a_{35} = 67
\]

Thus, the 35th term is:

\[
\boxed{67}
\]