Question
Find the 24th term of the sequence. 11, 16, 21....
Answers
GPT-4o mini
To find the 24th term of the sequence \(11, 16, 21, \ldots\), we first need to identify the pattern.
The sequence starts at 11 and increases by 5 each time:
- From 11 to 16, the increase is \(16 - 11 = 5\)
- From 16 to 21, the increase is \(21 - 16 = 5\)
This defines an arithmetic sequence where:
- The first term \(a = 11\)
- The common difference \(d = 5\)
The formula for the \(n\)th term of an arithmetic sequence is given by:
\[
a_n = a + (n - 1)d
\]
Substituting the known values into the formula to find the 24th term (\(n = 24\)):
\[
a_{24} = 11 + (24 - 1) \times 5
\]
\[
a_{24} = 11 + 23 \times 5
\]
Calculating \(23 \times 5\):
\[
23 \times 5 = 115
\]
Now substituting back:
\[
a_{24} = 11 + 115 = 126
\]
Thus, the 24th term of the sequence is \(\boxed{126}\).
The sequence starts at 11 and increases by 5 each time:
- From 11 to 16, the increase is \(16 - 11 = 5\)
- From 16 to 21, the increase is \(21 - 16 = 5\)
This defines an arithmetic sequence where:
- The first term \(a = 11\)
- The common difference \(d = 5\)
The formula for the \(n\)th term of an arithmetic sequence is given by:
\[
a_n = a + (n - 1)d
\]
Substituting the known values into the formula to find the 24th term (\(n = 24\)):
\[
a_{24} = 11 + (24 - 1) \times 5
\]
\[
a_{24} = 11 + 23 \times 5
\]
Calculating \(23 \times 5\):
\[
23 \times 5 = 115
\]
Now substituting back:
\[
a_{24} = 11 + 115 = 126
\]
Thus, the 24th term of the sequence is \(\boxed{126}\).