The formula given is as follows
[tex]a_{1}=-2, a_{n} = a_{n-1}+4, n\geq2[/tex]
Answer:
[tex]a_{n} = 4n - 6[/tex]
Step-by-step explanation:
Since it is given that [tex] n\geq 2[/tex]
[tex]a_{2} = a_{1}+4[/tex]
[tex]a_{3} = a_{2}+4[/tex]
... and so on...
we substitute [tex]a_{1}[/tex] to [tex] a_{2}[/tex] , [tex]a_{2} [/tex] to [tex]a_{3}[/tex] and so on.. we will get
[tex]a_{3} = a_{2} + 4 [/tex]
[tex]= a_{1} + 4 +4[/tex]
[tex]= a_{1} + 2(4)[/tex]
[tex]a_{4} = a_{3} + 4 [/tex]
[tex]= a_{1} + 2(4) +4[/tex]
[tex]= a_{1} + 3(4)[/tex]
and the patterns goes on.
We can see from the recursion pattern that
[tex]a_{n} = a_{1} + (n-1)(4)[/tex]
[tex]a_{n} = -2 + (n-1)(4)[/tex]
[tex]= -2 + 4n - 4[/tex]
[tex]= 4n - 6[/tex]
