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Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600

User Hemantvsn
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2 Answers

3 votes

Answer: Choice A 1,162.5

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Step-by-step explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

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Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

User Kirill Ilichev
by
5.9k points
5 votes

Answer:

A. 1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

User Phil Brubaker
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5.7k points