1. Describe and extend each sequence . A. The height, in feet , of windowsills in a high- rise building is represented by this sequence : 3,15,27,39,...

Describe the rule for the sequence .

Find the next two terms of the sequence . Show your work.

B. Mason put sticky notes on some pages of his math book. The page numbers form this sequence : 3,5,8,13,21,34,...

Describe the rule for the sequence.

Find the next two terms of the sequence Show your work

THE EXPLICIT FORMULA
2. Use the following arithmetic sequence and the formula a n =a 1 +(n-1)d to answer the questions below.
123, 116 6,109,102,95,...

Part 1: Find the value of each of the following:
a 1 =__ and d=__

Part 2: Find the explicit formula Show your work.

Part 3: Use the explicit formula you found in Part to find the value of the 100th term in the sequence, a 100 Show your work

3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence10 points: 5 points each) Formulas Anthmetic sequence Expick - 4 (1 Geometric sequence Expicit Recursive first term Recursive

Part 1: The total value of a collection of nickels can be described by this sequence: 5,10,15,20,25,30,...
Type of sequence :
Explicit formula:
Recursive formula:

Part II: The number of rats living in an abandoned building increases each year . The total number of rats can be described by this sequence: 2,6,18,54,162,... Type of sequence:
Explicit formula:
Recursive formula:

(c) The potential energy of the object decreases while the kinetic energy increases.

Step-by-step explanation:

Given that, an object falls through Earth's atmosphere.

As there is no friction of drag, this is the case of free fall.

So, there is no restriction in the motion of the object due to the air molecule. i.e there is no rubbing of air molecule with the object, so there is no possibility of heat (thermal energy) generation. So, the thermal energy of the object remains constant. So, options (a) and (d) are incorrect.

The only force that acts on the body is the gravitational force, as there is no drag. This force causes only the acceleration of the body. The shape of the body remains unaffected. So, there is no strain in the body. Hence, the elastic energy of the body is zero and there is no change in it. Option (b) is also incorrect.

Now, due to gravitational force, the object falls towards the earth, and its velocity increases. As the object moves towards the center of the Earth, so, the distance between the center of the earth and the object is decreases, which leads to a decrease in the potential energy of the object (as the potential energy of any object due to another body is directly proportional to the distance between the center of both the body).

While, the velocity of the object increases, so the kinetic energy of the object increases (as the kinetic energy of any object of directly proportional to the square of the velocity of the object).

Hence, the potential energy of the object decreases while the kinetic energy increases.

Therefore, option (c) is correct.