UPSKILL MATH PLUS

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A sequence is a function defined on the set of natural numbers \(\mathbb{N}\). A sequence is a function of form f:, where \(\mathbb{R}\) is the set of all real numbers.
If the sequence is of the form  \(a_1\), \(a_2\), \(a_3\), \(a_4\), ... then we can associate the function with the sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), ... by \(f (n) = a_n\), \(n = 1, 2, 3,\) …
 
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Let us solve a problem of sequence with a function to understand this concept.
Example:
The general term for a sequence is defined as f(n)=an=3n+4n+6. Find the first three terms \(a_1\), \(a_2\), a3.
 
Let us substitute the natural number \(n = 1, 2, 3, 4, ...\) in the given equation.
 
The first three terms are:
 
f(n)=an=3n+4n+6, where \(n = 1, 2, 3, 4, ...\)
 
a1=3(1)+41+6
 
=3+47
 
a1=77
 
a2=3(2)+42+6
 
=6+48
 
a2=108
 
a3=3(3)+43+6
 
=9+49
 
a3=139
 
Therefore, the first three terms are 77, 108 and 139.