Question

In an art gallery, the first row has 120 seats, and each row after the first has three more seats than the row before it. How many seats will be there in the 6th row by using the recursive formula?105115125135

Answer 1

`135`

Step-by-step explanation:

Here, we want to know the number of seats that will be on the 6th row

The 6th row is simply 5 rows ahead of the first row

Since each row is 3 seats more than the last, we have the recursive formula as:

`a_n\text{ = a}_(n-1)\text{ + 3}`

where:

an is the current row

an-1 is the row before the current

Finally, we have the number of seats as follows:

`\begin{gathered} a_1\text{ = 120} \\ a_2\text{ = 120 + 3 = 123} \\ a_3\text{ = 123 + 3 = 126} \\ a_4\text{ = 126 + 3 = 129} \\ a_5\text{ = 129 + 3 = 132} \\ a_6\text{ = 132 + 3 = 135} \end{gathered}`

This means that, on the 6th row, we would have 135 seats