Solve for a.

In an arithmetic sequence, the nth term an is given by the formula an=a1+(n−1)d, where a1 is the first term and d is the commo

Dmitry_Shevchenko [17]

Answer:

$a_{10} = \frac{10}{65536}$

Step-by-step explanation:

The first step to solving this problem is verifying if this sequence is an arithmetic sequence or a geometric sequence.

This sequence is arithmetic if:

$a_{3} - a_{2} = a_{2} - a_{1}$

We have that:

$a_{3} = 40, a_{2} = 10, a_{3} = \frac{5}{2}$

$a_{3} - a_{2} = a_{2} - a_{1}$

$\frac{5}{2} - 10 = 10 - 40$

$\frac{-15}{2} \neq -30$

This is not an arithmetic sequence.

This sequence is geometric if:

$\frac{a_{3}}{a_{2}} = \frac{a_{2}}{a_{1}}$

$\frac{\frac{5}[2}}{10} = \frac{10}{40}$

$\frac{5}{20} = \frac{1}{4}$

$\frac{1}{4} = \frac{1}{4}$

This is a geometric sequence, in which:

The first term is 40, so $a_{1} = 40$

The common ratio is $\frac{1}{4}$ , so $r = \frac{1}{4}$ .

We have that:

$a_{n} = a_{1}*r^{n-1}$

The 10th term is $a_{10}$ . So:

$a_{10} = a_{1}*r^{9}$

$a_{10} = 40*(\frac{1}{4})^{9}$

$a_{10} = \frac{40}{262144}$

Simplifying by 4, we have:

$a_{10} = \frac{10}{65536}$

3 0

4 years ago

William has 8 1/4 cups of fruit juice. If he divides the juice into 3/4 cup servings, how many servings will he have?

nikdorinn [45]

Answer: 11 servings

Step-by-step explanation:

To get the number of servings, all we need to do is divide 8 1/4 by 3/4

converting 8 1/4 to improper fraction will yield 33/4

8 1/4 ÷ 3/4

=33/4 ÷ 3/4

= 33/4 ÷ 4/3

The 4 at the numerator will cancel the 4 at the denominator. we will be left with;

=33/3 =11

Therefore, there will be 11 servings.

7 0

4 years ago

Read 2 more answers

A password is 4 characters long and must consist of 3 letters and one number. if letters cannot be repeated and the password mus

sdas [7]

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more number and variables.

The possibility of selecting the password = 26 * 25 * 24 * 10 = 156000

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

Find out more on equation at: brainly.com/question/2972832

#SPJ4

7 0

2 years ago

Which equation is equivalent to 16 Superscript 2 p Baseline = 32 Superscript p 3?.

Mrac [35]

The equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,

$2^{8p}=2^{5p+15}$

<h3>What is equivalent equation?</h3>

Equivalent equation are the expression whose result is equal to the original expression, but the way of representation is different.

Given information-

The given equation in the problem is,

$16^{2p}=32^{p+3}$

Write both the equation in the form of same base number as,

$(2^4)^{2p}=(2^5)^{p+3}$

The power of the power of a number can be written as product of both the numbers. Thus,

$(2)^{4\times2p}=(2)^{5\times(p+3)}\\2^{8P}=2^{5P+15}$

This is the required equation.

Now if the base is the same at both side of the expression, then the powers can be compared. Thus,

$8p=5p+15$

Solve it further to find the value of p as,

$8p-5p=15\\3p=15\\p=5$

Thus the equation which is equivalent to 16 Superscript 2 p Baseline equal to 32 Superscript p 3 is,

$2^{8p}=2^{5p+15}$

Learn more about the equivalent expression here;

brainly.com/question/2972832

7 0

3 years ago

What is the sum of measures of the exterior angles of a polygon that has fifteen sides

madreJ [45]

$\bf \textit{sum of exterior angles}\\\\ n\theta =360~~ \begin{cases} n=\textit{number of sides}\\ \theta = \textit{angle in degrees}\\[-0.5em] \hrulefill\\ n=15 \end{cases}\implies 15\theta =360 \\\\\\ \theta =\cfrac{360}{15}\implies \theta =24$

8 0

4 years ago