The fifth term of f(n) = n² - 3 is 22
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Further explanation
Firstly , 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 sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
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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 sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
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Given:
f(n) = n² - 3
Asked:
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]
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Learn more
- Geometric Series : https://brainly.com/question/4520950
- Arithmetic Progression : https://brainly.com/question/2966265
- Geometric Sequence : https://brainly.com/question/2166405
Answer details
Grade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
