Question

Julio is training for a swimming race. The first part of his training schedule is shown. Session 1 2 3 456 Swimming distance (mi) 0.25 0.55 0.85 1.15 1.45 1.75 Is this training schedule an arithmetic sequence? Explain. If Julio’s training schedule starts on a Tuesday and he swims every two days, on which day will he swim for 2.95 miles?

Answer 1

An arithmetic sequence is a sequence in which the difference between each consecutive term remains same (constant).  

The explicit formula for an arithmetic sequence is $A_n=a+(n-1)d$, where a is first term of sequence, d is the common difference between consecutive terms.

A) We can see from Julio's swimming distance that it is in arithmetic sequence as after every successive training session Julio's swimming distance increased by 0.30 miles.  

$0.55-0.25=0.30$

$0.85-0.55=0.30$

$1.75-1.45=0.30$

Therefore, we can see that Julio's training schedule is an arithmetic sequence.

B) Let us find Julio will take how many days to swim 2.95 miles by using explicit formula.

$A_n=a+(n-1)d$

Let us substitute our given information in above formula.

$2.95=0.25+(n-1)0.30$

$2.95=+0.25+0.30n-0.30$

$2.95=0.30n-0.05$

$2.95+0.05=0.30n$

$3.00=0.30n$  

$n=\frac{3.00}{0.30}=10$

We are told that Julio swims every two days, this implies that he would swim on alternate days. So he will swim 2.95 miles on 10*2 =20th day.

Let us find 20th day will be which day. As Julio started his training schedule on Tuesday, 20th day will be a Sunday. Therefore, Julio will swim for 2.95 miles on a Sunday.