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3 years ago

Find the nTH term of this sequence: 15, 12, 9, 6

Mathematics

2 answers:

shtirl [24]3 years ago

4 0

Answer:

-3n + 18

Step-by-step explanation:

an = dn + (a - d)

The difference is -3.

The first term is 15.

an = -3n + (15- (-3))

an = -3n + 15 + 3

an = -3n + 18

Elden [556K]3 years ago

3 0

Answer:

aₙ= 18 -3n

Step-by-step explanation:

15, 12, 9, 6

Given AP with first term= 15 and common difference= -3

aₙ=a₁+(n-1)d= 15+(n-1)*(-3)= 15 - 3n+3= 18-3n

aₙ= 18 -3n

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The seventh term of an arithmetic progression is equal to twice the fifth term. The sum

mario62 [17]

Answer:

a₁ = - 24

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₇ = 2a₅ , then

a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )

- a₁ - 2d = 0 → (1)

The sum to n terms of an AP is

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ]

Given $S_{7}$ = 84 , then

$\frac{7}{2}$ (2a₁ + 6d) = 84

3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )

2a₁ + 6d = 24 → (2)

Thus we have 2 equations

- a₁ - 2d = 0 → (1)

2a₁ + 6d = 24 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate d

- 3a₁ - 6d = 0 → (3)

Add (2) and (3) term by term to eliminate d

- a₁ = 24 ( multiply both sides by - 1 )

a₁ = - 24

6 0

3 years ago

De un grupo de 60 personas, la tercera parte finalizó la escuela primaria solamente, y las ⅖ partes completaron la secundaria. E

notka56 [123]

Answer:

36 personas

Step-by-step explanation:

las 2/5 partes q completaron secundaria tambien finalizaron primaria

con lo cual el tercio que estudio primaria esta dentro del grupo de personas que estudiaron

60*2/5 = 24

24 personas estudiaron

60-24=36

4 0

3 years ago

A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :

For the first parenthesis:

$x^{2}+6x+b^{2}$

We can rewrite this as:

$x^{2}+2(3)x+b^{2}$

Hence in this case $b=3$ and $b^{2}=9$ :

$x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}$

For the second parenthesis:

$y^{2}-8y+b^{2}$

We can rewrite this as:

$y^{2}-2(4)y+b^{2}$

Hence in this case $b=-3$ and $b^{2}=9$ :

$y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}$

Then, equation (5) is rewritten as follows:

$(x^{2}+6x+9)+(y^{2}-8y+16)=75+9+16$ (6)

Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.

Rearranging:

$(x-3)^{2}+(y-4)^{2}=100$ (7)

At this point we have the circle equation in the center radius form $(x-h)^{2} +(y-k)^{2}=r^{2}$

Hence:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

8 0

3 years ago

What is the reciprocal of 5 1/8

Mars2501 [29]

Answer:

0.19512195122

Step-by-step explanation:

3 0

3 years ago

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Heron’s formula: Area = square root 5(5-a)(5-b)(5-c) What is the area of triangle DFG? Round to the nearest whole square unit. 2

timurjin [86]

To do this problem, you will need to know the side lengths of the triangle. If you have those, just plug them in for a, b, and c and evaluate the square root.

Here is an example. If the sides are 3, 4, 5.
It would be:

$A= \sqrt{6(6-3)(6-4)(6-5))}$

The 6 is in the formula because it is the semi-perimeter (half).

3 0

3 years ago

Read 2 more answers