Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 4, 5, 6, 7, ... an = Submit

Answer 1

The given sequence is 4, 5, 6, 7, ... This is an arithmetic sequence where each term increases by 1.

To express this sequence in terms of \( n \), where \( n \) represents the term's position, we can observe that:

- The first term (\( n = 1 \)) is 4,
- The second term (\( n = 2 \)) is 5,
- The third term (\( n = 3 \)) is 6,
- The fourth term (\( n = 4 \)) is 7.

We can derive the expression for the \( n \)-th term (\( a_n \)) as follows:

\[
a_n = 4 + (n - 1)
\]

Simplifying this gives us:

\[
a_n = n + 3
\]

Therefore, the expression for the \( n \)-th term of the sequence is:

\[
a_n = n + 3
\]