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3 years ago

Determine whether the following sequence is arithmetic, geometric, or neither.

Mathematics

1 answer:

lawyer [7]3 years ago

5 0

Answer:

arith

Step-by-step explanation:

Let's check whether or not this is a geometric series.

The first term is 1 1/3, or 4/3.

What would the common ratio be, to convert this 4/3 into the 2nd term, 2?

(4/3)r = 2, or r = 2(3/4) = 6/4 = 3/2.

Assuming that the common ratio is r = 3/2, will multiplying 2 by 3/2 result in the 3rd term, 2 2/3? NO. So this is NOT a geometric progression.

The difference between 1 1/3 and 2 is 2/3. If we add 2/3 to 2, we get 2 2/3, which agrees with the given 3rd term.

If we add 2/3 to 2 2/3, do we get the fourth given term, 3 1/3?

2/3 + 2 2/3 is equivalent to 2 4/3, or 10/3, which is equivalent to 3 1/3.

Thus, this IS an arithmetic sequence, and the common difference is 2/3.

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Given:

An exam starts at 10:10 and lasts for 75 minutes.

To find:

The time when the exam end.

Solution:

We have,

Starting time = 10:10

Exam duration = 75 minutes

First we will divide the 75 minutes in two parts 50 minutes and 25 minutes.

We know that 50 minutes after 10:10 is 11:00 and 25 minutes after 11:00 is 11:25. So,

10:10 + 75 minutes = 10:10 + 50 minutes +25 minutes)

= (10:10 + 50 minutes) +25 minutes

= 11:00 +25 minutes

= 11:25

Therefore, the exam ends at 11:25.

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Step-by-step explanation:

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3 years ago

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4 years ago

Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00

Tatiana [17]

Answer:

The principal must be = $8991.88

Step-by-step explanation:

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P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

$15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88$

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3 years ago

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Answer:

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Step-by-step explanation:

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