Question
The bids in an online auction are represented by the arithmetic sequence shown below. Write a rule to represent the arithmetic sequence. What is the ninth bid?190, 200, 210, 220, ...
Answers
GPT-4o mini
The given sequence is an arithmetic sequence where the first term is \( a_1 = 190 \) and the common difference \( d = 200 - 190 = 10 \).
The general formula for the \( n \)-th term of an arithmetic sequence can be expressed as:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Substituting the known values into the formula:
\[
a_n = 190 + (n - 1) \cdot 10
\]
Now, to find the ninth bid (\( a_9 \)), we substitute \( n = 9 \) into the formula:
\[
a_9 = 190 + (9 - 1) \cdot 10
\]
\[
a_9 = 190 + 8 \cdot 10
\]
\[
a_9 = 190 + 80
\]
\[
a_9 = 270
\]
Therefore, the rule to represent the arithmetic sequence is
\[
a_n = 190 + (n - 1) \cdot 10
\]
And the ninth bid is \( 270 \).
The general formula for the \( n \)-th term of an arithmetic sequence can be expressed as:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Substituting the known values into the formula:
\[
a_n = 190 + (n - 1) \cdot 10
\]
Now, to find the ninth bid (\( a_9 \)), we substitute \( n = 9 \) into the formula:
\[
a_9 = 190 + (9 - 1) \cdot 10
\]
\[
a_9 = 190 + 8 \cdot 10
\]
\[
a_9 = 190 + 80
\]
\[
a_9 = 270
\]
Therefore, the rule to represent the arithmetic sequence is
\[
a_n = 190 + (n - 1) \cdot 10
\]
And the ninth bid is \( 270 \).