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).
4, comma, 13, comma, 22, comma, point, point, .
4,13,22,...
Find the 35th term.
Find the 35th term.

Answer 1

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 \( \boxed{310} \).