Pleaseeeee helpppppp meeeeee

What is the value of y in the sequence below? 2,y,18, -54,162,

snow_lady [41]

First, let's check if the sequence is geometric or arithmetric.

If arithmetric, the sequence will have common difference.

Arithmetric

$\displaystyle \large{a_{n + 1} - a_n = d}$

d stands for a common difference. Common Difference means that sequences must have same difference after subtracting.

Geometric

$\displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}$

r stands for a common ratio.

To find the value of y, you can check the sequence. If we try subtracting the sequences, the differences are different. That means the sequences are not arithmetric. That only leaves the geometric sequence.

Let's check by dividing sequences.

We have:

2,y,18,-54,162,...

Let's check by divide -54 by 18 and 162 by -54. We need to divide more than one so we can prove that the sequence is geometric.

$\displaystyle \large{ \frac{ - 54}{18} = - 3 } \\ \displaystyle \large{ \frac{ 162}{ - 54} = - 3}$

Hence, the sequence is geometric.

Because the common ratio is -3. Let these be the following:

$\displaystyle \large{ a_{n + 1} = y } \\ \displaystyle \large{ a_n = 2 } \\ \displaystyle \large{ r = - 3 }$

From the:

$\displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}$

Substitute the values in.

$\displaystyle \large{ \frac{y}{2} = - 3}$

Multiply the whole equation by 2 to isolate y.

$\displaystyle \large{ \frac{y}{2} \times 2 = - 3 \times 2} \\ \displaystyle \large{ y = - 6}$

Therefore, the value of y is -6.

7 0

2 years ago

What is an equation of a line,in point-slope from, that passes through (1, -7) and has a slope of -2/3

il63 [147K]

Answer:

y + 7 = - $\frac{2}{3}$ (x - 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

Where m is the slope and (a, b) a point on the line

Here m = - $\frac{2}{3}$ and (a, b) = (1, - 7), thus

y - (- 7) = - $\frac{2}{3}$ (x - 1), that is

y + 7 = - $\frac{2}{3}$ (x - 1) ← in point- slope form

3 0

2 years ago

3^x grows faster than x^3. Explain why.

Allisa [31]

Because 3 is a number and the x is unknow so its just an exponent the x ^ 3 grows three each time

3 0

3 years ago

Greg is designing a clock face. Using the center of the clock face as the origin, he keeps its diameter at 10 units. Match the p

Nat2105 [25]

The center of the clock is taken as the origin.The clock is a circle with a diameter 10 units.Radius is half the diameter .Radius = 10 ÷2= 5 units.

The clock is divided in four quadrants .On x axis y=0 and on y axis x=0.

When it is 12 o'clock the hour hand is on positive of y axis.Coordinates of the point at 12 o'clock=(0,5)

When it is 3 o 'clock the hour hand is on positive of x axis .Coordinate of the point at 3o'clock is (5,0)

When it is 6 o'clock the hour hand is on negative of y axis .The coordinates of the point at 6o'clock is (0,-5)

At 9o'clock the hour hand is on negative of x axis .The coordinate of the point at 6o'clock is(-5,0)

3 0

3 years ago

Read 2 more answers

Plz help me in here and tysm for ya help :3

lapo4ka [179]

It would cost somehow less than $1000 and you would know that because 347 students is a large number, but since it hold 44 students in each bus, it’ll take not to long to get to 347. So since each bus is $95, it would at least reach to 700+

(All is estimated)

8 0

3 years ago