Question
Write an explicit formula for the following sequence. Find the fifteenth term.14, 15, 16, 17, 18, ...Question content area bottomPart 1What is an explicit formula for the given sequence?
Answers
GPT-4o mini
The sequence provided is: 14, 15, 16, 17, 18, ...
This is an arithmetic sequence where the first term \( a_1 \) is 14 and the common difference \( d \) is 1 (since each term increases by 1).
The explicit formula for the \( n \)-th term of an arithmetic sequence can be given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Substituting the known values into the formula:
- \( a_1 = 14 \)
- \( d = 1 \)
We get:
\[
a_n = 14 + (n - 1) \cdot 1
\]
Simplifying this:
\[
a_n = 14 + n - 1
\]
\[
a_n = n + 13
\]
Thus, the explicit formula for the sequence is:
\[
a_n = n + 13
\]
Now, to find the fifteenth term \( a_{15} \):
\[
a_{15} = 15 + 13 = 28
\]
Therefore, the fifteenth term of the sequence is **28**.
This is an arithmetic sequence where the first term \( a_1 \) is 14 and the common difference \( d \) is 1 (since each term increases by 1).
The explicit formula for the \( n \)-th term of an arithmetic sequence can be given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Substituting the known values into the formula:
- \( a_1 = 14 \)
- \( d = 1 \)
We get:
\[
a_n = 14 + (n - 1) \cdot 1
\]
Simplifying this:
\[
a_n = 14 + n - 1
\]
\[
a_n = n + 13
\]
Thus, the explicit formula for the sequence is:
\[
a_n = n + 13
\]
Now, to find the fifteenth term \( a_{15} \):
\[
a_{15} = 15 + 13 = 28
\]
Therefore, the fifteenth term of the sequence is **28**.