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4 months ago

Q:
# 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 walksincreases by 20% each week. What is the sequence of the approximate distance that he will cover in each of the 5 weeks?A3.36 5.18 8.96 and 15.48B336.5.18, 7.46 and 10.75C3.36 4.32 5.18 and 6.22D.3 3.6.5.18, 7.46, and 15.48ResetSubmit

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A:

The sequence of the approximate distance that he will cover in eachof the 5 weeks is: 3 , 3.6 , 4.32 , 5.18 , 6.22 ⇒ answer CStep-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 weekAssume that Mike walks 100% in the first weekThe amount Mick walks increases by 20% each weekThe amount Mick walks in every week after the first week is 120% of the previous weekThe constant ratio between each two consecutive weeks is 120% = 120/100 = 1.20 The information above gives a geometric sequenceThe 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 twoconsecutive 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 eachof the 5 weeks is: 3 , 3.6 , 4.32 , 5.18 , 6.22Learn more:You can learn more about the nth term in brainly.com/question/1522572#LearnwithBrainly