Question

A swimmer is training for an upcoming meet. He swims 10 laps the first day. Each day he increases the number of laps he swims by 5. Which BEST describes the function?

Answer 1

10+5=15

He swam 15 laps the second day

Explanation:

Answer 2

The function is
`T_(n) = 5 + 5n`

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.

`T_(n) = a + (n - 1) d`

Where a = first term = 10 laps

n = number of days

d = common difference = 5

`T_(n) = The Function`

By Substitution

`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 \\`

Hence, the function is
`T_(n) = 5 + 5n`

where n = number of days