The sequence of the approximate distance that he will cover in each
of the 5 weeks is: 3 , 3.6 , 4.32 , 5.18 , 6.22 ⇒ answer C
Step-by-step explanation:
Micks doctor has suggested that he needs to walk for 5 weeks,
beginning with a total of 3 km in week 1. The amount Mick walks
increases by 20% each week
Assume that Mike walks 100% in the first week
- The amount Mick walks increases by 20% each week
- The amount Mick walks in every week after the first week is 120% of the previous week
- The constant ratio between each two consecutive weeks is 120% = 120/100 = 1.20
The information above gives a geometric sequence
The rule of the nth term of a geometric sequence is [tex]a_{n}=ar^{n-1}[/tex]
where a is the first term and r is the common ratio between each two
consecutive terms
∵ Mick needs to walk 3 km in the 1st week
∴ a = 3 ⇒ 1st term
∵ The amount Mick walks increases by 20% each week
- Use the constant ratio above
∴ r = 1.2
∴ [tex]a_{2}=(3)(1.2)^{2-1}[/tex]
∴ [tex]a_{2}=3.6[/tex]
∴ [tex]a_{3}=(3)(1.2)^{3-1}[/tex]
∴ [tex]a_{3}=4.32[/tex]
∴ [tex]a_{4}=(3)(1.2)^{4-1}[/tex]
∴ [tex]a_{4}=5.18[/tex]
∴ [tex]a_{5}=(3)(1.2)^{5-1}[/tex]
∴ [tex]a_{5}=6.22[/tex]
The sequence of the approximate distance that he will cover in each
of the 5 weeks is: 3 , 3.6 , 4.32 , 5.18 , 6.22
Learn more:
You can learn more about the nth term in brainly.com/question/1522572
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