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, dot dot dot
203,199,195,...
Find the 35th term.
Find the 35th term.

Answer 1

To identify the 35th term of the sequence given by 203, 199, 195, ..., we first observe the pattern in the sequence.

The terms decrease as follows:

- From 203 to 199, the difference is \( 203 - 199 = 4 \).
- From 199 to 195, the difference is \( 199 - 195 = 4 \).

This indicates that the sequence is an arithmetic sequence with a common difference of \(-4\).

The general formula for the \( n \)-th term of an arithmetic sequence can be expressed as:

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

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

For this sequence:
- \( a_1 = 203 \)
- \( d = -4 \)

To find the 35th term (\( n = 35 \)):
\[
a_{35} = 203 + (35 - 1) \cdot (-4)
\]

Calculating this step-by-step:
1. Calculate \( 35 - 1 = 34 \).
2. Calculate \( 34 \cdot (-4) = -136 \).
3. Finally, substitute this back into the formula:
\[
a_{35} = 203 - 136 = 67
\]

Thus, the 35th term of the sequence is:

\[
\boxed{67}
\]