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kkurt [141]
3 years ago
13

What is the value of the sum of all the terms of the geometric series 300, 60, 12, …?

Mathematics
1 answer:
ruslelena [56]3 years ago
3 0
<h3>Answer:   375</h3>

=========================================

Work Shown:

a = 300 = first term

r = 60/300 = 0.2 = common ratio

We multiply each term by 0.2, aka 1/5, to get the next term.

Since -1 < r < 1 is true, we can use the infinite geometric sum formula below

S = a/(1-r)

S = 300/(1-0.2)

S = 300/0.8

S = 375

----------

As a sort of "check", we can add up partial sums like so

  • 300+60 = 360
  • 300+60+12 = 360+12 = 372
  • 300+60+12+2.4 = 372+2.4 = 374.4
  • 300+60+12+2.4+0.48 = 374.4+0.48 = 374.88

and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.

----------

Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.

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What is the smallest positive integer N such that the value 70 + 30(N) is not a prime number?
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Woody and Jen were paid $60 to paint the garage. Jim started at 8 a.M. And Woody didn't arrive until 10 a.M. The work was comple
Dennis_Churaev [7]

Answer:

$36

Step-by-step explanation:

Jim worked from 8am - 2 pm , which is 6 hours

Woody worked form 10am - 2pm, which is 4 hours

If we take the total time (4+6 = 10) and divide the amount they got, we have:

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8 0
3 years ago
You take out $50,000 for loans during your college career. You must pay it back with 7% APR for 20 years, making monthly payment
Ad libitum [116K]

Answer:

The monthly payment for the loan amount for 20 years is $806.167

Step-by-step explanation:

The principal loan amount= $ 50,000

The rate of interest = 7 %

the time period of loan = 20 years = 20 × 12 = 240 months

let the amount after 20 years = $ A

<u>From Compounded method</u>

Amount = Principal × (1+\dfrac{\textrm rate}{100})^{\textrm Time}

or, A = 50,000 × (1+\dfrac{\textrm 7}{100})^{\textrm 20}

or, A = 50,000 × (1.07)^{20}

Or, A = 50,000 × 3.8696

∴ Amount = $ 193,480

So, The amount after 20 years = $ 193,480

The monthly payment amount = $ \frac{193480}{240} = $ 806.167

Hence The monthly payment for the loan amount for 20 years is $806.167 Answer

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Read 2 more answers
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