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