All categories

3 years ago

A rule for nth term of -2 , -5/4 ,-1/2,1/4

Mathematics

1 answer:

miv72 [106K]3 years ago

6 0

Answer:

Step-by-step explanation:

This is an arithmetic sequence

a1 = -2

Difference = 2nd term - first term

$=\frac{-5}{4}-[-2]\\\\=\frac{-5}{4}+2\\\\=\frac{-5}{4}+\frac{2*4}{1*4}\\\\=\frac{-5+8}{4}=\frac{3}{4}$

$a_{n}=a+(n-1)d\\\\=-2+(n-1)*(\frac{3}{4})\\\\=-2+\frac{3}{4}n-\frac{3}{4}\\\\=\frac{-2*4}{1*4}-\frac{3}{4}+\frac{3}{4}n\\\\=\frac{-8-3}{4}+\frac{3}{4}n\\\\=\frac{-11}{4}+\frac{3}{4}n$

You might be interested in

Use the following image to assist in your answer. a = - 6 - 9 - 4

vfiekz [6]

Step-by-step explanation:

Pythagoras' theorem for the smallest one :

$c^2 = 4^2 + 6^2$

$c^2 = 16 + 36$

$c^{2}$ = 52

Pythagoras' theorem for the middle one :

$b^{2}$ = $6^{2}$ + $a^{2}$

Pythagoras' theorem for the biggest one :

$(4+a)^2 = c^2 + b^2$

$16 + 8a + a^2 = 52 + b^2$

Using the formula before (for $b^2$ ) it becomes :

$16 + 8a + a^2 = 52 + (6^2 + a^2)$

$16 + 8a + a^2 = 52 + 6^2 + a^2$

$16 + 8a = 52 + 6^2$

16 + 8a = 52 + 36

16+8a = 88

8a = 88-16

8a = 72

$a = \frac{72}{8}$

a = 9

Verifying :

$b^2 = 6^2 + a^2$

$b^2 = 36 + 81$

$b^2 = 117$

$b^{2}$ = 117

The biggest one :

$(4+a)^2 = c^2 + b^2$

$(4+9)^2 = 52 + 117$

$13^2 = 169$

True

8 0

2 years ago

Question 1 of 10

Mnenie [13.5K]

Answer: A

Step-by-step explanation:

7 0

1 year ago

In 2000, the population of Massachusetts

Zepler [3.9K]

Answer:

The population reaches 7 million people in the year 2032.

Step-by-step explanation:

We have that

$f(x) = 6.3*(1.0032)^{x}$

Using this model, find the year when the population reaches 7 million people.

This is x years after 2000, in which x is found when f(x) = 7. So

$f(x) = 6.3*(1.0032)^{x}$

$7 = 6.3*(1.0032)^{x}$

$(1.0032)^{x} = \frac{7}{6.3}$

$(1.0032)^{x} = 1.11$

We have to following logarithm rule

$\log{a^{x}} = x\log{a}$

So we apply log to both sides of the equality

$\log{(1.0032)^{x}} = \log{1.11}$

$x\log{1.0032} = \log{1.11}$

$x = \frac{\log{1.11}}{\log{1.0032}}$

$x = 32.66$

2000 + 32.66 = 2032

The population reaches 7 million people in the year 2032.

3 0

2 years ago

Judy just calculated the standard deviation for a project she is working on. The value for the standard deviation is a small num

Contact [7]

Answer: b) The data is spread close to the mean

Step-by-step explanation: Theoretically, when the standard deviation of a statistical data is large or high, it simply means that the values in such statistical data set are farther away from the mean, On the other hand when the standard deviation is small or low, it simply means that the values of such statistical data are close to the mean of those data on average.

Therefore Judy's low standard deviation for her project simply indicates that her statistical data set is spread close to the mean.

7 0

2 years ago

Is it nice or not? vacations lice mice janury

Vikentia [17]

Vacation is nice January is nice

3 0

3 years ago