To determine the 35th term of the given sequence \(4, 13, 22, \ldots\), we first need to identify the pattern in the sequence.
Let's analyze the first three terms:
- The first term (\(a_1\)) is 4.
- The second term (\(a_2\)) is 13.
- The third term (\(a_3\)) is 22.
Next, we find the differences between consecutive terms:
- \(a_2 - a_1 = 13 - 4 = 9\)
- \(a_3 - a_2 = 22 - 13 = 9\)
The difference is consistent; each term increases by 9. This indicates that the sequence is an arithmetic sequence with a common difference \(d = 9\).
The formula for the \(n\)-th term of an arithmetic sequence is given by:
\[ a_n = a_1 + (n - 1) \cdot d \]
Here, \(a_1 = 4\) and \(d = 9\). We need to find the 35th term (\(n = 35\)):
\[ a_{35} = 4 + (35 - 1) \cdot 9 \]
Calculating further:
\[ a_{35} = 4 + 34 \cdot 9 \] \[ = 4 + 306 \] \[ = 310 \]
Thus, the 35th term of the sequence is \( \boxed{310} \).
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