Answer:
Tn = 2Tn-1 - Tn-2
Step-by-step explanation:
Before we can generate the recursive sequence, we need to find the nth term of the given sequence.
nth term of an AP is given as:
Tn = a+(n-1)d
If a17 = -40
T17 = a+(17-1)d = -40
a+16d = -40 ...(1)
If a28 = -73
T28 = a+(28-1)d = -73
a+27d = -73 ...(2)
Solving both equations simultaneously using elimination method.
Subtracting 1 from 2 we have:
27d - 16d = -73-(-40)
11d = -73+40
11d = -33
d = -3
Substituting d = -3 into 1
a+16(-3) = -40
a - 48 = -40
a = -40+48
a = 8
Given a = 8, d = -3, the nth term of the sequence will be
Tn = 8+(n-1) (-3)
Tn = 8+(-3n+3)
Tn = 8-3n+3
Tn = 11-3n
Given Tn = 11-3n and d = -3
Tn-1 = Tn - d... (3)
Tn-1 = 11-3n +3
Tn-1 = 14-3n
Tn-2 = Tn-2d...(4)
Tn-2 = 11-3n-2(-3)
Tn-2 = 11-3n+6
Tn-2 = 17-3n
From 3, d = Tn - Tn-1
From 4, d = (Tn - Tn-2)/2
Equating both common difference
(Tn - Tn-2)/2 = Tn - Tn-1
Tn - Tn-2 = 2(Tn - Tn-1)
Tn - Tn-2 = 2Tn-2Tn-1
2Tn-Tn = 2Tn-1 - Tn-2
Tn = 2Tn-1 - Tn-2
The recursive formula will be
Tn = 2Tn-1 - Tn-2
Answer:
Option B,C and E are solution to given inequality 
Step-by-step explanation:
We need to check which ordered pairs from given options satisfy the inequality 
Ordered pairs are solutions to inequality if they satisfy the inequality
Checking each options by pitting values of x and y in given inequality
A ) (1, -5)

So, this ordered pair is not the solution of inequality as it doesn't satisfy the inequality.
B) (-3, - 2)

So, this ordered pair is solution of inequality as it satisfies the inequality.
C) (0, -9)

So, this ordered pair is solution of inequality as it satisfies the inequality.
D) (2, -1)

So, this ordered pair is not the solution of inequality as it doesn't satisfy the inequality.
E) (5, 4)

So, this ordered pair is solution of inequality as it satisfies the inequality.
So, Option B,C and E are solution to given inequality 
Y ≤ x - 5
y ≥-x - 4
x - 5 = -x - 4
+ x + x
2x - 5 = -4
+ 5 + 5
2x = 1
2 2
x = ¹/₂
y = x - 5
y = ¹/₂ - 5
y = -4¹/₂
The following points that lie in the solution set to the following system of inequalities is (¹/₂, -4¹/₂).