Answer:
The closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]
Step-by-step explanation:
Given that the first term [tex]a_{1}=0.3[/tex] and [tex]a_{n+1}=a_{n}+0.75[/tex]
To find the closed linear form for the given sequence
The formula for arithmetic sequence is
[tex]a_{n}=a_{1}+(n - 1)d[/tex] (where d is the common difference)
The above equation is of the given form [tex]a_{n+1}=a_{n}+0.75[/tex]
Comparing this we get d=0.75
With [tex]a_{1}=0.3[/tex] and d=0.75
We can substitute these values in [tex]a_{n}=a_{1}+(n - 1)d[/tex]
[tex]a_{n}=a_{1}+(n - 1)d[/tex]
[tex]=0.3+(n-1)(0.75)[/tex]
[tex]=0.3+0.75n-0.75[/tex]
[tex]=-0.45+0.75n[/tex]
Rewritting as below
[tex]=0.75n-0.45[/tex]
Therefore [tex]a_{n}=0.75n-0.45[/tex]
Therefore the closed linear form of the given sequence is [tex]a_{n}=0.75n-0.45[/tex]