The numbers of seats in the first 12 rows of a high school auditorium form and arithmetic sequence the first row nine seats second row has 11

a) The recursive formula for the number of seats in the n th row will be; 

S1 = 9

S(n) = S (n-1) +2 

b) Explicit formula; is that of an arithmetic progression; such that if a is the first term , and d is the common difference , then the n th term will be given by the formula:  a + (n-1) d; where a is 9, and d is 2

Hence; for n th row = 9+ 2(n-1)

c) Number of seats in 12 th row using the formula in b.

 n = 12 , a = 9, d = 2

therefore; 9 + 2(12-1)

             = 9 + 2(11)

             = 31 seats 

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

how is that middle school

step-by-step explanation: