Answer:
Step-by-step explanation:
As the given recursive formula
[tex]{\displaystyle a_{n}=a_{n-1}+2n}[/tex]
and
[tex]a_{1} =-6[/tex]
So, we have to determine the next three terms i.e. [tex]a_{2}, a_{3},a_{4}[/tex]
Determining the value of [tex]a_{2}[/tex]
As
[tex]{\displaystyle a_{n}=a_{n-1}+2n}[/tex]
Putting [tex]n = 2[/tex] to find [tex]a_{2}[/tex]
[tex]{\displaystyle a_{2}=a_{2-1}+2(2)}[/tex]
[tex]{\displaystyle a_{2}=a_{1}+4}[/tex]
[tex]{\displaystyle a_{2}=(-6)+4}[/tex] ∵a₁=-6
[tex]{\displaystyle a_{2}=-2}[/tex]
Determining the value of [tex]a_{3}[/tex]
As
[tex]{\displaystyle a_{n}=a_{n-1}+2n}[/tex]
Putting [tex]n = 3[/tex] to find [tex]a_{3}[/tex]
[tex]{\displaystyle a_{3}=a_{3-1}+2(3)}[/tex]
[tex]{\displaystyle a_{3}=a_{2}+6}[/tex]
[tex]{\displaystyle a_{3}=(-2)+6}[/tex] ∵a₂=-2
[tex]{\displaystyle a_{3}=4}[/tex]
Determining the value of [tex]a_{4}[/tex]
As
[tex]{\displaystyle a_{n}=a_{n-1}+2n}[/tex]
Putting [tex]n = 4[/tex] to find [tex]a_{4}[/tex]
[tex]{\displaystyle a_{4}=a_{4-1}+2(4)}[/tex]
[tex]{\displaystyle a_{4}=a_{3}+8}[/tex]
[tex]{\displaystyle a_{4}=(4)+8}[/tex] ∵a₃=4
[tex]{\displaystyle a_{4}=12}[/tex]
So,
Keywords: sequence, recursive formula, terms
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