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2 years ago

Find the sum of the first 50 terms of the sequence -6, -2, 2, 6

Mathematics

1 answer:

monitta2 years ago

4 0

Answer:

4600

Step-by-step explanation:

STEP 1: Determine type of progression

$d1 = - 2 - ( - 6) \\ d1 = 4 \\ \\ d2 = 2 - ( - 2) \\ d2 = 4$

Since d1 = d2, it is Arithmetic progression, with a common difference of 4

STEP 2: Evaluate the sum

$s = \frac{n}{2} (2a + (n - 1)d) \\ s = \frac{50}{2} (2( - 6) + (50 - 1)4) \\ s = 4600$

You might be interested in

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 7y = sin(x)

Elza [17]

The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65

4 0

2 years ago

I'm confused. Help. Find x please.

miss Akunina [59]

Answer:

x = 2 and x = 10

Step-by-step explanation:

(x+3)^2 = (x - 5)^2 + (x + 2)^2

x^2 + 6x + 9 = x^2 - 10x + 25 + x^2 + 4x + 4

x^2 + 6x + 9 =2x^2 - 6x + 29

x^2 - 12x + 20 = 0

(x - 10)(x - 2) = 0

x - 10 = 0; x = 10

x - 2 = 0; x = 2

4 0

2 years ago

If no number can be used more than once, how many different 2-digit numbers can be formed from the digits 4, 6, and 8?

ikadub [295]

Answer:

Six.

Step-by-step explanation:

hoped this helped!

4 0

2 years ago

1/5x-2/3y=30<br> What is the value of the x in the equation when y=15

svetlana [45]

Answer:

$\frac{1}{5} x - \frac{2}{3} y = 30 \\ \frac{1}{5} x - \frac{2}{3} 15 = 30 \\ \frac{1}{5} x - \frac{30}{3} = 30 \\ \frac{1}{5} x - 10 = 30 \\ \frac{1}{5} x = 30 + 10 \\ \frac{1}{5} x = 40 \\ x = 40 \div \frac{1}{5} \\ x = 40 \times \frac{5}{1} \\ x = 40 \times 5 \\ x = 200$

I hope I helped you^_^

8 0

2 years ago

Read 2 more answers

A Crayon is shown here.

Aleks04 [339]

The volume of the single crayon is 89.5 cm³, then the total volume of the crayons will be 2148 cm³. Then the correct option is D.

<h3>What is Geometry?</h3>

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A Crayon is shown here.

There are 24 crayons in a box.

The approximate total volume of the crayons will be

Total Volume of crayons = 24 × volume of the single crayon

The crayon is the combination of the cone and the cylinder

Then the volume of the single crayon (V₁) will be

$\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times r^2 \times h \right ) + \left ( \pi \times r^2 \times h \right )\\\\\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times 1.5^2 \times 2 \right ) + \left ( \pi \times 1.5^2 \times 12 \right )\\\\V_1 = 4.712 + 84.82\\\\V_1 = 89.535 \approx 89.5$

Then the Total volume will be

Total volume = 24 × 89.5

Total volume = 2148 cm³

More about the geometry link is given below.

brainly.com/question/7558603

#SPJ1

3 0

1 year ago