Answer: 

<u>Step-by-step explanation:</u>
a) This is an arithmetic sequence where 3 is added to the previous term.
48 + 3 = 51
51 + 3 = 54
54 + 3 = 57
The recursive formula for this sequence is:
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b) This is a geometric sequence where 2.5 is multiplied to the previous term.
100(2.5) = 250
250 (2.5) = 625
625(2.5) = 1562.5
The recursive formula for this sequence is: 
Divide 120 by 4 to get 1/9 of the rope: 30. Then multiply it by 9 to get the part after 1/4 was given away: 270. Now divide it by 3 to get 90 and lastly, multiply it by 4 to get a final answer of 360 centimeters. Hope this helps!
Answer:
The larger angle is 54°
Step-by-step explanation:
Given
Let the angles be: θ and α where
θ > α
Sum = 72
α : θ = 1 : 3
Required
Determine the larger angle
First, we get the proportion of the larger angle (from the ratio)
The sum of the ratio is 1 + 3 = 4
So, the proportion of the larger angle is ¾.
Its value is then calculated as:.
θ = Proportion * Sum
θ = ¾ * 72°
θ = 3 * 18°
θ = 54°