Question

Write an expression to describe the sequence below, and then find the 87th term. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

58, 59, 60, 61, ...


an =


a87 =

Answer 1

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

To describe the sequence, we can use the formula for the \( n \)-th term of an arithmetic sequence:

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

where:
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term position.

In this case:
- \( a_1 = 58 \)
- \( d = 1 \)

Substituting these values into the formula gives us:

\[
a_n = 58 + (n - 1) \cdot 1
\]

This simplifies to:

\[
a_n = 58 + n - 1
\]
\[
a_n = n + 57
\]

Now, we can find the 87th term (\( a_{87} \)):

\[
a_{87} = 87 + 57
\]
\[
a_{87} = 144
\]

Thus, the expressions and results are:

\[
a_n = n + 57
\]
\[
a_{87} = 144
\]