Question

Given the sequence below, and that sequence has a domain of n 2 1, find the fifth

Answer 1

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.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

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.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

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:

$\texttt{for } n \geq 1 :$

$f(n) = n^2 - 3$

$f(5) = 5^2 - 3$

$f(5) = 25 - 3$

$f(5) = \boxed{22}$

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Learn more

• Geometric Series : brainly.com/question/4520950
• Arithmetic Progression : brainly.com/question/2966265
• Geometric Sequence : brainly.com/question/2166405

Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term