Question

write an expression to describe the sequence below, and then find the 13th term. use n to represent the position of a term in the sequence, where n = 1 for the first term. 60, 120, 180, 240, ... a_n = a_{13} =

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence since the common difference \( d \) between consecutive terms is constant. Let's find the common difference: \( 120 - 60 = 60 \), \( 180 - 120 = 60 \), \( 240 - 180 = 60 \). So, the common difference \( d = 60 \).

Step2: Find the general formula for an arithmetic sequence

The general formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term and \( d \) is the common difference. Here, \( a_1 = 60 \) and \( d = 60 \). Substituting these values into the formula:
\[

$$\begin{align*} a_n &= 60 + (n - 1) \times 60 \\ &= 60 + 60n - 60 \\ &= 60n \end{align*}$$

\]

Step3: Find the 13th term

To find the 13th term, substitute \( n = 13 \) into the formula \( a_n = 60n \):
\[
a_{13} = 60 \times 13 = 780
\]

Answer:

\( a_n = 60n \)
\( a_{13} = 780 \)