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).
3, comma, 11, comma, 19, comma, dot dot dot
3,11,19,...
Find the 38th term.
Find the 38th term.
3, comma, 11, comma, 19, comma, dot dot dot
3,11,19,...
Find the 38th term.
Find the 38th term.
Answers
GPT-4o mini
To find the 38th term of the sequence given by the first three terms: 3, 11, 19, we first need to identify the pattern in the sequence.
The differences between successive terms are:
- \(11 - 3 = 8\)
- \(19 - 11 = 8\)
This indicates that the sequence is arithmetic with a common difference of \(8\).
The general formula for the nth term \(a_n\) of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
where:
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.
In this case:
- \(a_1 = 3\)
- \(d = 8\)
Now plug in \(n = 38\):
\[
a_{38} = 3 + (38 - 1) \cdot 8
\]
\[
a_{38} = 3 + 37 \cdot 8
\]
\[
a_{38} = 3 + 296
\]
\[
a_{38} = 299
\]
Thus, the 38th term of the sequence is \(299\).
The differences between successive terms are:
- \(11 - 3 = 8\)
- \(19 - 11 = 8\)
This indicates that the sequence is arithmetic with a common difference of \(8\).
The general formula for the nth term \(a_n\) of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
where:
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.
In this case:
- \(a_1 = 3\)
- \(d = 8\)
Now plug in \(n = 38\):
\[
a_{38} = 3 + (38 - 1) \cdot 8
\]
\[
a_{38} = 3 + 37 \cdot 8
\]
\[
a_{38} = 3 + 296
\]
\[
a_{38} = 299
\]
Thus, the 38th term of the sequence is \(299\).