Answer:
The function is [tex]T_{n} = 5 + 5n[/tex]
Step-by-step explanation:
Options are missing; I'll find the function of swimmer in relation to days
Topic: Arithmetic Progression
Given
First day = 10 laps
Increment = 5 laps daily
To get the function of the number of days, we make use of the arithmetic progression formula.
[tex]T_{n} = a + (n - 1) d[/tex]
Where a = first term = 10 laps
n = number of days
d = common difference = 5
[tex]T_{n} = The Function[/tex]
By Substitution
[tex]T_{n} = a + (n - 1) d ---- Substitute\\ T_{n} = 10 + (n - 1) 5 \\T_{n} = 10 + 5n - 5\\T_{n} = 10 - 5 + 5n \\T_{n} = 5 + 5n \\[/tex]
Hence, the function is [tex]T_{n} = 5 + 5n[/tex]
where n = number of days
