Question

Write an expression to describe the sequence below, and then find the 62nd term. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

62, 63, 64, 65, ...


an =


a62 =

Answer 1

The sequence provided is an arithmetic sequence where each term increases by 1. We can express the \( n \)-th term of the sequence with the following formula:

\[
a_n = 61 + n
\]

Here's the breakdown:
- The first term (\( n = 1 \)) is \( 61 + 1 = 62 \).
- The second term (\( n = 2 \)) is \( 61 + 2 = 63 \).
- The third term (\( n = 3 \)) is \( 61 + 3 = 64 \).
- And so on.

Now, to find the 62nd term (\( a_{62} \)):

\[
a_{62} = 61 + 62 = 123
\]

Therefore, the answers are:

\[
a_n = 61 + n
\]
\[
a_{62} = 123
\]