Write the First Six Terms of the Sequence Beginning with the Given

question 31

Multiple Choice

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model,a quadratic model,or neither.​ $\begin{array} { l } a _ { 0 } = 4 \\a _ { n } = \left( a _ { n - 1 } \right) ^ { 2 }\end{array}$ ​

• A)0,4,-16,256,-65,536,4,294,967,296 First differences: -228,65,040,-4,294,836,480, \(2 \times 10 ^ { 19 }\)
• Second differences: 12,240,65,280,4,294,901,760, \(2 \times 10 ^ { 19 }\)
• Linear
• B)0,4,16,256,65,536,4,294,967,296 First differences: 12,240,65,280,4,294,901,760, \(2 \times 10 ^ { 19 }\)
• Second differences: -228,65,040,-4,294,836,480, \(2 \times 10 ^ { 19 }\)
• Quadratic
• C)4,-16,256,-65,536,4,294,967,296,-18,446,744,073,709,600,000 First differences: -228,65,040,-4,294,836,480, \(2 \times 10 ^ { 19 }\)
• Second differences: 12,240,65,280,4,294,901,760, \(2 \times 10 ^ { 19 }\)
• Neither
• D)4,16,256,65,536,4,294,967,296,18,446,744,073,709,600,000 First differences: 12,240,65,280,4,294,901,760, \(2 \times 10 ^ { 19 }\)
• Second differences: 228,65,040,4,294,836,480, \(2 \times 10 ^ { 19 }\)
• Neither
• E)0,-4,16,-256,65,536,-4,294,967,296 First differences: 12,240,65,280,4,294,901,760, \(2 \times 10 ^ { 19 }\)
• Second differences: -228,65,040,-4,294,836,480, \(2 \times 10 ^ { 19 }\)
• Quadratic

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Definitions:

μm

Micrometer, a unit of length in the metric system equal to one millionth of a meter, used to measure small distances, such as those in biological cells and structures.

Total Magnification

The combined magnifying power of an optical system, calculated by multiplying the objective lens magnification by the ocular lens magnification.

Ocular Lens

A transparent structure in the eye that, along with the cornea, helps to refract light to be focused on the retina.

Objective Lens

The lens in a microscope closest to the specimen that helps to magnify the image of the object being observed.