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 ![a_{n}=ar^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Dar%5E%7Bn-1%7D)
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
∴ ![a_{2}=(3)(1.2)^{2-1}](https://tex.z-dn.net/?f=a_%7B2%7D%3D%283%29%281.2%29%5E%7B2-1%7D)
∴ ![a_{2}=3.6](https://tex.z-dn.net/?f=a_%7B2%7D%3D3.6)
∴ ![a_{3}=(3)(1.2)^{3-1}](https://tex.z-dn.net/?f=a_%7B3%7D%3D%283%29%281.2%29%5E%7B3-1%7D)
∴ ![a_{3}=4.32](https://tex.z-dn.net/?f=a_%7B3%7D%3D4.32)
∴ ![a_{4}=(3)(1.2)^{4-1}](https://tex.z-dn.net/?f=a_%7B4%7D%3D%283%29%281.2%29%5E%7B4-1%7D)
∴ ![a_{4}=5.18](https://tex.z-dn.net/?f=a_%7B4%7D%3D5.18)
∴ ![a_{5}=(3)(1.2)^{5-1}](https://tex.z-dn.net/?f=a_%7B5%7D%3D%283%29%281.2%29%5E%7B5-1%7D)
∴ ![a_{5}=6.22](https://tex.z-dn.net/?f=a_%7B5%7D%3D6.22)
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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