MATH SOLVE

3 months ago

Q:
# Given the sequence below, and that sequence has a domain of n 2 1, find the fifthterm.f(n) = n2 β 3

Accepted Solution

A:

The fifth term of f(n) = nΒ² - 3 is 22[tex]\texttt{ }[/tex]Further explanationFirstly , let us learn about types of sequence in mathematics.Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.[tex]\boxed{T_n = a + (n-1)d}[/tex][tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]Tn = n-th term of the sequenceSn = sum of the first n numbers of the sequencea = the initial term of the sequenced = common difference between adjacent numbers[tex]\texttt{ }[/tex]Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.[tex]\boxed{T_n = a ~ r^{n-1}}[/tex][tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]Tn = n-th term of the sequenceSn = sum of the first n numbers of the sequencea = the initial term of the sequencer = common ratio between adjacent numbersLet us now tackle the problem![tex]\texttt{ }[/tex]Given:f(n) = nΒ² - 3Asked:f(5) = ?Solution:[tex]\texttt{for } n \geq 1 :[/tex][tex]f(n) = n^2 - 3[/tex][tex]f(5) = 5^2 - 3[/tex][tex]f(5) = 25 - 3[/tex][tex]f(5) = \boxed{22}[/tex][tex]\texttt{ }[/tex]Learn moreGeometric Series : Progression : Sequence : detailsGrade: Middle SchoolSubject: MathematicsChapter: Arithmetic and Geometric SeriesKeywords: Arithmetic , Geometric , Series , Sequence , Difference , Term