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

question 19

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. ​
A₁ = 3
​a_n = an _{- 1} - n

• A)0,3,1,-2,-6,-11 First differences: 3,-2,-3,-4,-5
• Second differences: -1,-1,-1,-1
• Quadratic
• B)0,3,1,-2,-6,-11,-17 First differences: -2,-3,-4,-5,-6
• Second differences: 1,1,1,1
• Linear
• C)3,1,-2,-6,-11,-17 First differences: -2,-3,-4,-5,-6
• Second differences: 1,1,1,1
• Quadratic
• D)3,1,-2,-6,-11,-17 First differences: -2,-3,-4,-5,-6
• Second differences: -1,-1,-1,-1
• Quadratic
• E)0,3,1,-2,-6,-11 First differences: 3,-2,-3,-4,-5
• Second differences: 1,1,1,1
• Quadratic

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Definitions:

Grouped Data

Data that has been organized into groups or categories, often to simplify analysis and identify patterns within the data set.

Ungrouped Data

Data that has not been organized into groups or categories and is presented in its raw form.

Bell-Shaped

Describes the graphical shape of a distribution that is symmetrical and has a single peak in the middle, resembling a bell; commonly associated with the normal distribution.

Standard Deviation

An index quantifying the spread or variability among a collection of numbers, where a smaller standard deviation suggests the numbers are closely clustered around the average.