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3 years ago

Write a recursive formula for the sequence -2,4,-8, 16, ...

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

5 0

Answer:

$a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2$

Step-by-step explanation:

The first number in the sequence, $a_1$ , is -2.

Each number after that is the previous number multiplied by -2.

$a_1 = -2$

$a_2 = a_1 \times (-2) = -2 \times (-2) = 4$

$a_3 = a_2 \times (-2) = 4 \times (-2) = -8$

etc.

$a_n = -2a_{n - 1}$

We start by stating that $a_1 = -2$ .

Now we need to show that for all n greater than or equal to 2, each number in the sequence is the previous number multiplied by -2.

$a_n = -2a_{n - 1}$

Answer:

$a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2$

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Plz answer asap I rlly need help

Alex17521 [72]

Answer:

-8/10, -3/16, 3/16

Step-by-step explanation:

5 0

3 years ago

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T

Ad libitum [116K]

Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180 ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

$60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}$

$105^{\circ}+ m\angle B=180^{\circ}$

Simplify:

$m\angle B=75^{\circ}$

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.

$\frac{\sin A}{BC} = \frac{\sin C}{AB}$

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

$\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}$

then,

$BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}$

$BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798$ unit

Similarly for AC:

$\frac{\sin B}{AC} = \frac{\sin C}{AB}$

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

$\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}$

then,

$AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}$

$AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283$ unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

i,e

Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

$A = \frac{1}{2} \times AB \times AC \times \sin A$

Substitute the values in above formula to get area;

$A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}$

$A = 4 \times 10.9283 \times 0.86602540378$

Simplify:

Area of triangle ABC = 37.856 (approx) square unit

4 0

3 years ago

andres has 10 more goldfish than todd. Together,they have 50 goldfish.How many goldfish does each boy have?

Dmitry [639]

Let's go ahead and construct an equation to show this. Together, they have 50 goldfish. This can be represented as =50.

Since we don't know how many Todd has, we're going to make a variable. We'll name it T, for Todd.

What about Andres? How many does he have? 10 more than Todd. Well, if Todd's amount is T, and Andres has 10 more, we can express that as T+10.

Now, just put the two pieces together! T+10=50.

The next step is inverse operations. You want to find out how many T is, so you need to get rid of the 10. To take 10 away from something is doing what? Subtraction! Be warned, though; whatever you do to one side of the problem, you have to do to the other. 10-10 is 0, and 50-10 is 40. Since we took the 10 away and 50 is now 40, what you're left with is T=40.

Wait a second.. wasn't "T" Todd's amount? Yep! That means that Todd has 40 goldfish. And we already know that Andres has 10, so there's your answer!

3 0

3 years ago

Read 2 more answers

X^2 - 36 = 0.

strojnjashka [21]

Answer:

(x+6)(x−6)=0

x=-6 or x=6

Step-by-step explanation:

X^2 - 36 = 0

Solve by Square Root

add 36 both sides

x^2−36+36=0+36

x^2=36

square root

x=±√36

x=6 or x=−6

You can do that or for 2nd option

Solve by factoring

x^2-36=0

(x+6)(x−6)=0

Set factors equal to 0

x+6=0 or x−6=0

x=-6 or x=6

PLEASE NOTE: 36 is the square of 6

and

x2 is the square of x1

8 0

3 years ago

Helppppppppppppppppppppppppppppp

GalinKa [24]

Answer:
x = 4

Explanation:
For the right hand side:
log base 9 of 8 + log base 9 of (x-2) = log base 9 (8*(x-2))
= log base 9 of (8x-16)
For the left hand side:
2*log base 9 of x = log base 9 of x^2

Now, equating the two sides and solving for x:
log base 9 of (8x-16) = log base 9 of x^2
This means that:
x^2 = 8x - 16
x^2 - 8x + 16 = 0
(x-4)^2 = 0
Therefore:
x = 4

Hope this helps :)

7 0

3 years ago