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).
2, comma, 7, comma, 12, comma, point, point, .
2,7,12,...
Find the 46th term.
Find the 46th term.

Answer 1

To solve for the 46th term of the sequence given the first three terms \(2, 7, 12\), we first need to identify a pattern or formula based on these terms.

1. **Identify the Differences**:
- The first term is \(2\).
- The second term is \(7\).
- The third term is \(12\).

Now, let's calculate the differences between consecutive terms:
- \(7 - 2 = 5\)
- \(12 - 7 = 5\)

The difference between consecutive terms is constant and equals \(5\).

2. **Recognize the Formula**:
Since the difference is constant, this is an arithmetic sequence. An arithmetic sequence can be described by the formula:
\[
a_n = a_1 + (n-1)d
\]
where \(a_n\) is the \(n\)th term, \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
- Here, \(a_1 = 2\) and \(d = 5\).

3. **Calculate the 46th Term**:
To find the 46th term \(a_{46}\):
\[
a_{46} = 2 + (46-1) \times 5
\]
\[
= 2 + 45 \times 5
\]
\[
= 2 + 225
\]
\[
= 227
\]

Thus, the 46th term of the sequence is \( \boxed{227} \).