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:
Step-by-step explanation:
The direction of movement of Jordan on his birthday forms a right angle triangle. His movement from his house to his parents due south represents the opposite side of the right angle triangle. His movement due west represents the adjacent side and the movement back home along the straight line, d represents the hypotenuse. To determine d, we would apply the Pythagorean theorem. Thus
d² = 6² + 4² = 52
d = √52 = 7.2 km
The total distance that he drove on his birthday is
6 + 4 + 7.2 = 17.2 km
Answer:
(-3, -3) ?
Step-by-step explanation:
it looks like you already answered your question
-10 -9 -8 -6 -5 -4 -3 -2 -1 0 1 2 3 4
Go back -5 places and you will land on the answer of -8
Hope this helps! :)
