What is the mean of -14,-10,-1,and -10?

Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}

iren [92.7K]

Answer:

A) a_n = 5n + 2

B) a_n = (2^(n + 1)) - 1

Step-by-step explanation:

A) The sequence is given as;

{7,12,17,22,27,...}

The differences are:

5,5,5,5.

This is an arithmetic sequence following the formula;

a_n = a_1 + (n - 1)d

d is 5

Thus;

a_n = a_1 + (n - 1)5

Now, a_1 = 7. Thus;

a_n = 7 + 5n - 5

a_n = 5n + 2

B) The sequence is given as;

{ 3,7,15,31,63,...}

Now, let's write out the differences of this sequence:

Differences are:

4, 8, 16, 32

This shows that it is a geometric sequence with a common ratio of 2.

In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15

Thus, a_2 = 2a_1 + 1

Also, a_(2 + 1) = 2a_2 + 1

Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1

Thus; a_n can be expressed as:

a_n = (2^(n + 1)) - 1

7 0

3 years ago

Please help work this equation

Flauer [41]

Hi!

<u>Given these two equations:</u>

$x = y + 8$

$x + 4 = 2(y + 4)$

We want to solve using the substitution method. Knowing that x is equal to y + 8, we can simply plug in 'y + 8' in for x in the second equation, like so:

$(y+8)+4=2(y+4)$

Combine like terms on both sides:

$y+12=2y+8$

Subtract y from both sides:

$12=y+8$

Subtract 8 from both sides:

$y=4$

Now, we can simply plug the y value in to the first equation, and solve for x:

$x=4+8$

Simplify:

$x=12$

<h3>Therefore, x is equal to 12 and y is equal to 4.</h3>

<u>Learn more about the substitution (and also elimination!) method here:</u>

brainly.com/question/14619835

4 0

2 years ago

Alma had four ants in her ant farm. She found three more ants outside and put them in the ant farm. She wanted to know how many

olga2289 [7]

Answer:

42

Step-by-step explanation:

4+3=7 7x6=42

5 0

3 years ago

26 ptss!! select the expressions that are equivalent to the expression below.

valkas [14]

Answer:

1st, 2nd, and last.

Step-by-step explanation:

For the first two common rules can be applied such as $n\sqrt{a/b}$ = $\frac{\sqrt[n]{a} }{\sqrt[n]{b} }$ and that $\sqrt[n]{\frac{a}{b} } = (\frac{a}{b})^{n}$

and for the last one this is just simplifying the radical and if you factor it you realize that, $\frac{750}{512} = \frac{5^3}{8^3}*6$ meaning that you can take the radical off of 5/8 and end up with that final answer

7 0

3 years ago

George says that 4+ a +a+a+b+b=24ab

antoniya [11.8K]

Answer:

3a+2b+4

Step-by-step explanation:

24ab indicates that there is 24 of unit ab which there is not. there is 4+ 3a+2b

4 0

2 years ago