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?

Answer 1

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**.