Ask question

Ask question

All categories

3 years ago

6

Write a formula for the general term or nth term for the sequence. Then find the indicated term. five halves comma five fourths

comma five eighths comma five sixteenths ...; a 8 a Subscript nequals ?

1 answer:

nadya68 [22]3 years ago

6 0

Sequence: 5/2, 5/4, 5/8, 5/16
a8=?

a1=5/2
a2=5/4
a3=5/8
a4=5/16

a2/a1=(5/4)/(5/2)=(5/4)*(2/5)=(5*2)/(4*5)=2/4=1/2
a3/a2=(5/8)/(5/4)=(5/8)*(4/5)=(5*4)/(8*5)=4/8=1/2
a4/a3=(5/16)/(5/8)=(5/16)*(8/5)=(5*8)/(16*5)=8/16=1/2
Ratio: r=a2/a1=a3/a2=a4/a3→r=1/2

an=a1*r^(n-1)
a1=5/2, r=1/2
an=(5/2)*(1/2)^(n-1)
an=(5/2)*[1^(n-1)/2^(n-1)]
an=(5/2)*[1/2^(n-1)]
an=(5*1)/[2*2^(n-1)]
an=5/2^(1+n-1)
an=5/2^n

n=8→a8=5/2^8
a8=5/256

Answers:
The formula for the general term or nth term for the sequence is an=5/2^n
a8=5/256

You might be interested in

A student is 7 years old. If you triple the teachers age and add the student's age the answer is 163. How old is the teacher?

pogonyaev

Answer:

52

Step-by-step explanation:

We can write this out as an equation. Let's say that the teacher's age is x. Triple the teachers age plus the students age is 163, which can be written out as:

$3x + 7 = 163$

We want to isolate the variable, so subtract 7 from both sides. This gives us:

$3x = 156$

Finally, we divide both sides by 3, giving:

$x=52$

So the teacher is 52 years old.

Hope this helps!

4 0

2 years ago

Read 2 more answers

The question is below thanks

Paha777 [63]

Answer:

FH ~ 10.02

Step-by-step explanation:

1. Approach

One should first find the circumference of the given circle. Then one should find how large the fraction of the circumference one is supposed to find is. Finally, one should multiply the fraction of the circumference one is supposed to find by the total circumference.

2. Circumference of the circle

The formula for circumference is;

$2r$ π

Substitute in the given values;

It is given that the radius is, hence

2 (7) π

14π

3. Find the fraction of the circumference one is supposed to find

It is given that the angles over the measure of the total degrees of angles in a circle are equal to the arc surrounding the angles of the circumference. Essentially;

$\frac{angles}{360}=\frac{arc}{circumference}$

Substitute in the given information and solve;

$\frac{82}{360}=\frac{arc}{14pi}$

arc = $\frac{41}{180}*14pi$

arc = $\frac{287}{90}*pi$

arc ~ 10.02

3 0

3 years ago

If you ride your bike 12 miles per hour, how long would it take<br> you to travel 72 miles ?

poizon [28]

Answer:

It would take 6 hours for you to travel 72 miles.

Step-by-step explanation:

This question can be solved by a simple rule of three.

We have that:

Each hour, you ride 12 miles.

How many hours will take for you to travel 72 miles?

So:

1 hour - 12 miles

x hours - 72 miles

12x = 72

x = 72/12

x = 6

It would take 6 hours for you to travel 72 miles.

4 0

2 years ago

Find the final total value of a 10-year investment of $3600 at a simple annual rate of

joja [24]

Answer:kk

The final balance is $4,590.35.

The total compound interest is $990.35.

Step-by-step explanation:

5 0

3 years ago

Simplify this please

Ugo [173]

Answer:

$\frac{12q^{\frac{7}{3}}}{p^{3}}$

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. $(a^{x})^{n} = a^{xn}$

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). $a^{-x} = \frac{1}{a^{x}}$ , and to help with this question: $\frac{a^{-x}b}{1} = \frac{b}{a^{x}}$ .

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. $(a^{x})(a^{y}) = a^{x+y}$

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. $\frac{a^{x}}{a^{y}} = a^{x-y}$

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}$

$\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}$ Distribute exponent

$=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}$ Simplify each exponent by multiplying

$=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}$ Negative exponent rule

$=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}$ Combine the like terms in the numerator with the base "q"

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}$ Rearranged for you to see the like terms

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}$ Multiplying exponents with same base

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}$ 2 + 1/3 = 7/3

$=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}$ Fractional exponents as radical form

$=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.

$=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Multiply 4 and 3

$=\frac{12pq^{\frac{7}{3}}}{p^{4}}$ Dividing exponents with same base

$=12p^{(1-4)}q^{\frac{7}{3}}$ Subtract the exponent of 'p'

$=12p^{(-3)}q^{\frac{7}{3}}$ Negative exponent rule

$=\frac{12q^{\frac{7}{3}}}{p^{3}}$ Final answer

Here is a version in pen if the steps are hard to see.

5 0

3 years ago