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Vilka [71]
3 years ago
5

Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary.

Mathematics
1 answer:
sladkih [1.3K]3 years ago
5 0

Answer:

Answer is -759/5

Step-by-step explanation:

To find the sum of a finite geometric series, use the formula,  

Sn= a1-a1r^n/ 1-r

where n is the number of terms, a1 is the first term and r is the common ratio .  

common ratio = a2/a1

S8=3-3(-2/3)8 / 1-(-2/3)

S8 = 3-(-2)8/ 1+ 2/3

S8= 3-256/ 3+2/3

S8= -253/5/3

S8= -253*3/5

S8= -759/5

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alexandr1967 [171]

Answer:

1/4

Step-by-step explanation:

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3 0
2 years ago
Hot dogs come in packages of 10 and hot dog buns come in packages of 8 . What is the least amount of product that you need to Bu
lubasha [3.4K]

This exercise is solved by finding the least common multiple between 10 and 8.


In fact, you have to buy a certain number h of hot dog package, and you will have 10h hot dogs, since there are 10 hot dogs in each package. The key concept here is that the number of hot dogs you have in the end is a multiple of the number of hot dogs in each box.


Similarly, you have to buy a certain number b of hot dog buns package, and you will have 8b hot dogs, since there are 8 hot dog buns in each package. Again, the key concept here is that the number of hot dog buns you have in the end is a multiple of the number of hot dog buns in each box.


Then, you want to have the same number of hot dogs and hot dog buns, i.e. you want


10h = 8b


but you also want h and b to be the first values to satisfy this equation.


This means that you want a multiple of 10 to equal a multiple of 8, and you want the smallest possible number which does the trick. Again, this is exactly the definition of the least common multiple.


To find the least common multiple of two numbers, find their prime factorization, and collect all the primes from both factorizations, with the highest exponent possible. Since 10 = 2\cdot 5 and 8 = 2^3, the primes appearing are 2 and 5. The higher exponent for 2 is 3, and the only exponent for 5 is 1. So, the answer is 2^3\cdot 5 = 40.


So, if you buy 4 packages of hot dogs and 5 packages of hot dog buns, you will have 40 hot dogs and 40 hot dog buns, as requested.

4 0
3 years ago
Read 2 more answers
tony is taking a 5 year loan in the amount of $15,000. The interest is continuously compounded at an annual rate of 7%. How much
kobusy [5.1K]

Answer:

$21,038.28

Step-by-step explanation:

Use the equation 15000(1.07)^5 since 1.07 equals to 7% and you are loaning more money to Tony's account for 5 years.  You should get $21,038.28 as your result.

7 0
2 years ago
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abruzzese [7]

Answer:

if am correct your answer will be letter d

Step-by-step explanation:

6 0
2 years ago
How much material will Dmitri's mom need for the tent, including the floor?
suter [353]
<h3>Answer:  21.4 square meters</h3>

Work Shown:

A = area of the front triangular face

A = base*height/2

A = 2*1.7/2

A = 1.7

L = lateral area

L = (perimeter of the base)*(depth)

L = (2+2+2)*(3)

L = 18

SA = total surface area of a triangular prism

SA = 2*A+L

SA = 2*1.7+18

SA = 21.4 square meters

7 0
2 years ago
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