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.

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

7th term = 24

Step-by-step 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

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

what are ur choices?