Question

An auditorium has 12 seats in the front row. Each successive row, moving towards the back of the auditorium, has 2 additional seats. The last row has 80 seats. Write a recursive formula for the number of seats in the nth row and use the formula to find the number of seats in the 7thth row.

Answer 1

Recursive formula;a_n = [a_(n - 1)] + 2

7th term = 24

Explanation:

This is an arithmetic progression question that follows the formula;

A_n = a + (n - 1)d

Where;

A_n is the nth term

a is first term

n is total number of terms

d is the difference

We are told that front row has 12 seats

Thus; a1 = 12

Difference in number of seats as we progress is 2. Thus, d = 2

Now, recursive formula is given by;

a_n = [a_(n - 1)] + d

So in this case, recursive formula is;

a_n = [a_(n - 1)] + 2

Now, a1 = 12

Thus;

a_2 = [a_(2 - 1)] + 2

a_2 = (a_1) + 2

a_2 = 12 + 2

a_2 = 14

Similarly;

a_3 = (a_2) + 2

a_3 = 14 + 2

a_3 = 16

a_4 = (a_3) + 2

a_4 = 16 + 2

a_4 = 18

a_5 = (a_4) + 2

a_5 = 18 + 2

a_5 = 20

a_6 = (a_5) + 2

a_6 = 20 + 2

a_6 = 22

a_7 = (a_6) + 2

a_7 = 22 + 2

a_7 = 24