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:

Method of Loci

A mnemonic technique that involves associating items to be remembered with specific physical locations.

Positive Transfer

The beneficial effect of prior learning on the acquisition of new skills or knowledge.

Negative Transfer

A learning phenomenon where learning in one context or task hinders performance in another due to similarities that confuse the learner.

Decay

The process by which information is lost over time from memory, especially when it is not rehearsed or reviewed.