Answer:
The required recursive formula is:

Step-by-step explanation:
We are given a geometric sequence as:
6,-18,54,-162,.....
Clearly after looking at different terms of the sequence we could observe that the sequence is an geometric progression (G.P.) with common ratio= -3 denoted by r.
Let
represents the nth term of the sequence.
This means that:

As the common ratio is -3.
so,

Hence, the required recursive formula for the geometric sequence is:

3:4 = G:B
1:5 = Mr. Smith's class: 7th Grade
2:7= 7th: Middle school
12 girls = 3 units
1 unit = 12/3= 4
Boys = 4x4= 16
<em>Whole class = 28 students</em>
Class : Grade = 1:5 <em> 7 = number of units in Mr. Smith's class</em>
28 = 1 unit
5 units= 28x5= 140 <em>There are 140 kids in the grade</em>
140 = 2 units
1 unit = 140/2= 70
70x7=490
<u><em>There are 490 students in the whole grade</em></u>
Slope = (5+7)/(1-4) = 12/-3 = -4
slope = -4
y = mx + b
-7 = -4(4) + b
-7 = -16 + b
b = 9
equation
y = -4x + 9
The matrix

has eigenvalues
such that





for all values of
, so we need to have
in order for
to be real-valued. This happens for

where
is any integer, and over the given interval we have
and
.