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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.

3, 4, 5, 6, ...

an =

Answer 1

The sequence you provided is an arithmetic sequence where each term increases by 1.

To express the \( n^{th} \) term of the sequence, we can start from the first term, which is 3, and then add \( n - 1 \) to it (since for \( n = 1 \), we don't add anything).

Thus, the expression for the \( n^{th} \) term \( a_n \) can be written as:

\[ a_n = 3 + (n - 1) \]

This simplifies to:

\[ a_n = n + 2 \]

So, the formula for the \( n^{th} \) term of the sequence is:

\[ a_n = n + 2 \]