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​, ...

Answer 1

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 \( 270 \).