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2 years ago

These are the first six terms of a sequence starting with a1 = 80:

Mathematics

1 answer:

Nikitich [7]2 years ago

6 0

Answer:

$a _{n} = a( {r}^{n - 1} ) \\ a _{n} = 80(2 {}^{n - 1} ) \\ a _{n} = \frac{80. {2}^{n} }{ {2}^{ 1} } \\a _{n} = 40( {2}^{n} ) \\ a _{n} = ( {2}^{3} \times 5)( {2}^{n} ) \\ a _{n} = 5( {2}^{n + 3} )$

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Continuing the pattern, what do the following terms equal?

rodikova [14]

The series formed by using exponential property we get : $\frac{1}{2} , \frac{1}{4} , \frac{1}{8} ,\frac{1}{16} ,\frac{1}{32} ,\frac{1}{64} ,\frac{1}{128} ,\frac{1}{256} ,\frac{1}{512} ,\frac{1}{1024} .$

What is Exponential Property?

Properties of Exponents : It is also called power or degree.
It tells us how many times the base will be multiplied by itself.
The properties of exponents or laws of exponents are wont to solve problems involving exponents.
These properties also are considered as major exponents rules to be followed while solving exponents.

Using exponential property on given values we get,

$2^1=1/ 2\\2^2=1/4\\2^3=1/8\\2^4= 1/16\\2^5= 1/32\\2^6 = 1/64\\2^7 = 1/128\\2^8 = 1/256\\2^9 = 1/512\\2^10 = 1/1024\ ...$

Complete series using exponent property is: $\frac{1}{2} , \frac{1}{4} , \frac{1}{8} ,\frac{1}{16} ,\frac{1}{32} ,\frac{1}{64} ,\frac{1}{128} ,\frac{1}{256} ,\frac{1}{512} ,\frac{1}{1024} ,$

Learn more about exponential property here:

brainly.com/question/25633462

#SPJ9

4 0

1 year ago

What is the value of x/3y , when x = 18 and y = 3?

tekilochka [14]

So when you work with variables (x, y or any other letter), when they're beside a number it usually means to multiply.

So 3y can also be written as 3(3). So 3 multiplied by 3 is equal to 9

So now our problem looks like this,

x/9.

Since we already know what x is equal to, our problem will look like this

18/9.

So now all we have to do is divide.

18 divided by 9 is 2

So therefore, your answer is 2.

I hope this helps :)

3 0

3 years ago

The slope of the graph of y = -6x is _______

Andrei [34K]

Answer:

Step-by-step explanation:

slope = -6

y-intercept=0

3 0

3 years ago

Read 2 more answers

What is the value of y? A. 120° B. 66° C. Cannot be determined D. 60°

lesya692 [45]

The answer is D because all sides are equal and it’s a equilateral triangle

6 0

2 years ago

Student council expects $150 students for a dance and spends $10 on food for each student. The council expects the number of stu

Natalija [7]

Answer:

$A) S(t)=150(1.08)^{t-1}$ $B) A(t)=10(0.96)^{t-1}$

$C) If\:t = 1\\E(t)=150\times10\\ \\If\:t >1\\E(t)=150(1.08)^{t-1}\times10(0.96)^{t-1}$

Step-by-step explanation:

Considering that The Student Council expects to 150 students for a dance, and spends $10 per student.

If the expectancy is that the number of students increases by 8%

Then since the growth is 8%

we can write the the Predicted Number of Students as a Geometric Sequence,

$a_{1}=150\\a_{2}=150\times 1.08 =162\\a_{3}=162\times 1.08= 174.96\approx 175\\a_{4}=175\times1.08=189\\a_{5}=189\times 1.08=204.12\approx 204\\$

Therefore,

$S(t)=150(1.08)^{t-1}$

B) If we spend $10 per student on the 1st year, but the Council wants to reduce the expenditure 4% yearly. Since we want to reduce 4% we must multiply by 96%.

$b_{1}=10\\b_{2}=10*(0.96)=9.6\\b_{3}=9.6*(0.96)=9.22\\b_{4}=9.22*(0.96)=8.85\\b_{5}=8.85*(0.96)=8.50$

Therefore we can write:

$A(t)=10(0.96)^{t-1}$

The total expenditure for food must be reduced, by 4%. As long as the public goes increasing by 8% yearly this

So,

$If\:t = 1\\E(t)=150\times10\\ \\If\:t >1\\E(t)=150(1.08)^{t-1}\times10(0.96)^{t-1}$

7 0

2 years ago