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, dot dot dot
4,13,22,...
Find the 35th term.
Find the 35th term.

Answer 1

To find the 35th term of the sequence given by the first three terms: 4, 13, and 22, we first need to identify the pattern in the sequence.

Let's analyze the differences between the terms:

- The difference between the second term (13) and the first term (4) is:
\[
13 - 4 = 9
\]

- The difference between the third term (22) and the second term (13) is:
\[
22 - 13 = 9
\]

The differences between consecutive terms are consistent, with both differences being 9. This indicates that the sequence is an **arithmetic sequence**.

In an arithmetic sequence, each term can be defined by the formula:
\[
a_n = a_1 + (n - 1) \cdot d
\]
where \( a_n \) is the \( n \)-th term, \( a_1 \) is the first term, \( n \) is the term number, and \( d \) is the common difference.

Here, we have:
- \( a_1 = 4 \)
- \( d = 9 \)

We want to find the 35th term \( a_{35} \):
\[
a_{35} = 4 + (35 - 1) \cdot 9
\]
Calculating this gives:
\[
a_{35} = 4 + 34 \cdot 9
\]
Calculating \( 34 \cdot 9 \):
\[
34 \cdot 9 = 306
\]
Now, substituting this back:
\[
a_{35} = 4 + 306 = 310
\]

Thus, the 35th term of the sequence is:
\[
\boxed{310}
\]