Question

or Watch a video 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. 43, 44, 45, 46, ... an =

Answer 1

The sequence provided is an arithmetic sequence where each term increases by 1 from the previous term.

To express the \( n \)-th term (\( a_n \)) of this sequence, we can observe that the first term is 43. The general formula for an arithmetic sequence can be written as:

\[
a_n = a_1 + (n - 1) \cdot d
\]

where:
- \( a_1 \) is the first term,
- \( d \) is the common difference between terms (in this case, \( d = 1 \)),
- \( n \) is the term position.

Substituting in the values we have:

- \( a_1 = 43 \)
- \( d = 1 \)

The expression becomes:

\[
a_n = 43 + (n - 1) \cdot 1
\]

This simplifies to:

\[
a_n = 43 + n - 1 = n + 42
\]

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

\[
\boxed{a_n = n + 42}
\]