Can someone just check this to make sure it is correct and please be honest because my grade depends on this

Step2247 [10]

Answer:

$a_{n}=12n-8$

Step-by-step explanation:

We have been given a recurrence relation $a_{n+1}=a_{n}+12$ and the first term of the sequence $a_{1}=4$ .

We can rewrite the given recurrence relation as: $a_{n+1}-a_{n}=12$

We know that if difference between two consecutive terms is always constant, the sequence is called an arithmetic sequence. So we are dealing with an arithmetic sequence with first term as 4 and common difference as 12.

We can therefore, write an explicit formula for nth terms of the sequence as.

$a_{n}=a_{1}+(n-1)d\\a_{n}=4+(n-1)(12)\\a_{n}=4+12n-12\\a_{n}=12n-8\\$

This is the required explicit function rule for the given sequence.

4 0

3 years ago

Select all the ratios that are equivalent to the ratio 12:3. explain how you know( show multiplication or division)

grigory [225]

Answer:

C 4:1

D 24:6

F 1200:300

Step-by-step explanation:

The given ratio is $\frac{12}{3}$

Simplify

Divide by 3 both numerator and denominator

$\frac{4}{1}$

Verify each case

case A) we have

$\frac{6}{1}$

Compare with the given ratio

$\frac{6}{1} \neq \frac{4}{1}$

therefore

The ratio is not equivalent

case B) we have

$\frac{1}{4}$

Compare with the given ratio

$\frac{1}{4} \neq \frac{4}{1}$

therefore

The ratio is not equivalent

case C) we have

$\frac{4}{1}$

Compare with the given ratio

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

therefore

The ratio is equivalent

case D) we have

$\frac{24}{6}$

Simplify

Divide by 6 both numerator and denominator

$\frac{4}{1}$

Compare with the given ratio

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

therefore

The ratio is equivalent

case E) we have

$\frac{15}{6}$

Simplify

Divide by 3 both numerator and denominator

$\frac{5}{2}$

Compare with the given ratio

$\frac{5}{2} \neq \frac{4}{1}$

therefore

The ratio is not equivalent

case F) we have

$\frac{1,200}{300}$

Simplify

Divide by 300 both numerator and denominator

$\frac{4}{1}$

Compare with the given ratio

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

therefore

The ratio is equivalent

case G) we have

$\frac{112}{13}$ ----> irreducible

Compare with the given ratio

$\frac{112}{13} \neq \frac{4}{1}$

therefore

The ratio is not equivalent

3 0

3 years ago

Find the length of the missing side (nearest tenth). 15 yd 26 yd

Illusion [34]

Not enough data to be able to get an answer

7 0

3 years ago

What is the shaded region of 14m & 8m

natali 33 [55]

Area is length x width.
With this one, what we have to do is work out the area of the larger square and the smaller, inside square, and take one from the other.

The larger one is 14 x 14 = 196.
The smaller one is 8 x 8 = 64
So, 196 - 64 = 132m²

4 0

3 years ago

What is the point-slope form of a line with slope -5 that contains the point (2, -1)?

Arisa [49]

Point slope formula:
$y-y_1=m(x-x_1)$
We know that:
y1=-1
x1=2
m=-5
So we plug those into the formula
$y-(-1)=-5(x-2)$
negative + negative= positive so..
Final answer:
 $y+1=-5(x-2)$

8 0

4 years ago

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