Question

Write an expression to describe the sequence below, and then find the 93rd term. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

50, 100, 150, 200, ...


an =


a93 =

Answer 1

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:

\[
a_n = 50n
\]

\[
a_{93} = 4650
\]