The sequence you've provided is an arithmetic sequence where the first term \( a_1 = 50 \) and the common difference \( d = 50 \).
The general formula for the \( n \)-th term of an arithmetic sequence is:
\[ a_n = a_1 + (n - 1)d \]
Substituting the values we have:
\[ a_n = 50 + (n - 1) \cdot 50 \]
This simplifies to:
\[ a_n = 50 + 50n - 50 = 50n \]
So the expression for the \( n \)-th term is:
\[ a_n = 50n \]
Next, to find the 93rd term, we substitute \( n = 93 \) into the expression:
\[ a_{93} = 50 \cdot 93 \]
Calculating this gives:
\[ a_{93} = 4650 \]
Thus, the results are:
\[ a_n = 50n \]
\[ a_{93} = 4650 \]
1 answer