Write the first few terms of the sequence.
f₁ = 6
f₂ = f₁ + 5 = 11
f₃ = f₂ + 5 = 16
f₄ = f₃ + 5 = 21
and so on
The sequence is
6, 11, 16, 21, ...,
This is an arithmetic sequence with a common difference of 5.
In function notation, the sequence is
[tex]f_{n+1} = 6 + 5n, \\ \, n=0,1,2, \, ...,[/tex]
This represents the equation of a straight line with n as the independent variable and f as the dependent variable.
The slope is 5.
A graph of the line is shown below.
Answer:
The sequence is [tex]f_{n+1} = 6 + 5n, \,\, n=0,1,2, \, ...,[/tex]
The slope is 5.
