Example: A recovering heart attack patient is told to walk a certain distance each week. The patient walks 5 km the first week, 8 km the second week, 11 km the third week, and so on for 10 weeks. How many km did the patient walk on the 10th week?
Answer (1)
To determine how many kilometers the patient walked on the 10th week, we need to identify the pattern or rule in the sequence of distances walked each week. The sequence given is as follows: 5 km, 8 km, 11 km, and so on.
Step-by-step solution:
Identify the Pattern:
The patient increases their walking distance each week by the same amount. By examining the sequence:
From 5 km to 8 km, the increase is 3 km.
From 8 km to 11 km, the increase is also 3 km.
Therefore, it's an arithmetic sequence where the common difference, d , is 3 km.
Formula for the nth term of an Arithmetic Sequence:
The formula to find the n -th term of an arithmetic sequence is: a n = a 1 + ( n − 1 ) im es d where:
a n is the n -th term,
a 1 is the first term,
d is the common difference,
n is the term number.
Substitute the Known Values:
Here, a 1 = 5 , d = 3 , and n = 10 (for the 10th week): a 10 = 5 + ( 10 − 1 ) im es 3 a 10 = 5 + 9 im es 3 a 10 = 5 + 27 a 10 = 32
Therefore, on the 10th week, the patient walked 32 kilometers .
