Question

Johnnie begins a regullar walking program as a art of his new exercise routine. The first week he walks a distance of 5 km, 8 km the second week, 11 km the third week, 14 km the fourth week and so on for a period of 12 weeks. How far will Johnnie walk during the 12th week?
a) Explain why this sequence is an arithmetic sequence.



b) Write out the sequence using blanks where appropriate.


c) Write the explicit formula for the sequence.


d) How far will the patient walk during the 12th week?

Answer 1

a) Explain why this sequence is an arithmetic sequence.

It is an arithmetic progression since it is a succession of numbers such that the difference of any pair of successive terms in the sequence is constant, in this case, it is 3.

b) Write out the sequence using blanks where appropriate.

Week|Distance

   1           5

   2          8

   3          1 1

   4          14

    .           .

    .           .

    .           .

c) Write the explicit formula for the sequence.

an = a1 + d*(n -1)

an = 5 + 3*(n - 1)

an = 5 + 3*n  - 3

an = 3*n + 2

d) How far will the patient walk during the 12th week?

a12 = 3*12 + 2

a12 =  38

that is to say, in that week I walk 38 km