Given:
The sequence is:
[tex]6, -24, 96, -384,...[/tex]
To find:
The explicit formula for the given sequence and then find the 16th term.
Solution:
We have,
[tex]6, -24, 96, -384,...[/tex]
The ratio between two consecutive terms are:
[tex]\dfrac{-24}{6}=-4[/tex]
[tex]\dfrac{96}{-24}=-4[/tex]
[tex]\dfrac{-384}{96}=-4[/tex]
The given sequence has a common ratio. So, the given sequence is a geometric sequence with first term 6 and common ratio [tex]-4[/tex].
The explicit formula of a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]a=6, r=-4[/tex] in the above formula, we get
[tex]a_n=6(-4)^{n-1}[/tex]
We need to find the 16th term. So, put [tex]n=16[/tex] in the above formula.
[tex]a_n=6(-4)^{16-1}[/tex]
[tex]a_n=6(-4)^{15}[/tex]
[tex]a_n=6(-1073741824)[/tex]
[tex]a_n=-6442450944[/tex]
Therefore, the explicit formula for the given sequence is [tex]a_n=6(-4)^{n-1}[/tex] and 16th term of the given sequence is [tex]-6.442450944[/tex].
mathematic question
Answer:
i cant see it
Step-by-step explanation:
Answer: im hungry for sum points to eat hmmmmmm
Step-by-step explanation:
Shante is calculating the amount of time it takes a rocket to get to the moon. The moon is around 239,000 miles from Earth. How many hours would it take a rocket that can travel at 200 miles per minute to travel to the moon? Round to the nearest hour.
Answer:
20 hours
Step-by-step explanation:
Mathematically we know that;
time = distance/ speed
distance = 239,000 miles
Time = 200 miles per minute
time = 239,000/200 = 1195 minutes
Let us convert this to hours by dividing by 60 (since 60 minutes equal an hour
So we have 1195/60 = 19.91
This is approximately 20 hours
Answer:
D
Step-by-step explanation:
20 hours
A trinket factory can produce 3000 trinkets per day the. warehouse has a capacity of 50000 trinkets .currently there are 8000 trinkets in the warehouse assume that no trinkets are going to be shipped out of the warehouse for a while
Answer:
14 days
Step-by-step explanation:
Since there are already 8000 trinkets in the warehouse, this means that we need to find the number of days it will take for the factory to create 42,000 trinkets which would cause the warehouse to max out it's capacity.
50,000 - 8000 = 42,000 trinkets
Since the factory can produce 3000 trinkets per day, we simply need to divide 42,000 by 3000 to get the number of days before the warehouse is at max capacity
42,000 / 3000 = 14 days
Therefore, it will take 14 days for the warehouse to be filled
If the number of students taking online courses is increasing at a rate of 7% per
year, how long would it take for the number of students taking online courses to
double?
a) about 28.57 years
b) about 2.8 years
c) about 14.3 years
d) about 10.24 years
Answer:
it will take about 14.3 years
6 g of butter is used for making a cupcake. How many such cakes can be made by using 3 kg of butter?
Answer: 500
Step-by-step explanation:
Given
6 g butter is required to make a cupcake
If there is 3 kg butter
We know, 1 kg is equivalent to 1000 g i.e. 3 kg is 3000 gm
No of cup-cakes made
[tex]\Rightarrow \dfrac{3000}{6}=500\ \text{cupcakes}[/tex]
PLEASE SOMEONE HELP ME FIGURE OUT THESE 4 Ill give you brainiest!
Answer: 5. 83 1/3*pi, or 261.8 (approx.) 6. 2*pi, or 6.28 (approx.) 7. 42 2/3*pi or 134.04 (approx.) 8. 144*pi or 452.39 (approx.)
Step-by-step explanation:
Volume of a circular cone : pi*r^2*h/3
I applied the formula to find these answers
You roll a 6-sided die.
What is P(4)?
1/6 or 4/9 or 4/5 or 3/4
Answer:
1/6
Step-by-step explanation:
Because there is only a side that has the number 4 in a total of 6 sides
it takes 2 1/2 cups of sugar to make 4 dozen sugar cookies. How much sugar is needed to make 120 sugar cookies
Answer:
6.25 cups of sugar
Step-by-step explanation:
Let's make a proportion expression:
2.5/48 = x/120
Let x be the amount of sugar needed to make 120 sugar cookies.
Cross multiply:
120*2.5=48x
48x=300
x=6.25
So, you would need 6 1/4 cups or 6.25 cups of sugar to make 120 sugar cookies.
work out
(10 - 3 * 2)
Answer:
4
Step-by-step explanation:
(10 - 3*2)
negative 3 times 2 = -6
10 minus 6 = 4
Work Out The Answers
Answer:
A1.) 87 + 63 =150
180 - 150 = 30
all the As is the same formula....
B1.) 180 - 123 = 57
57 + 82 = 139
180 - 131 = 41
Find the area of the shape.
5 ft
2 ft
3 ft
10 ft
The area of the composite shape is
square feet
Answer
300
Step-by-step explanation:
multiply by each other
7x2-6x=-7
Solve using quadratic formula :)
The midpoint of AB‾AB is M(−4,−3)M(−4,−3). If the coordinates of A are (−1,-2)(−1,−2), what are the coordinates of B?
Answer:
(-7, -4)
Step-by-step explanation:
The midpoint formula is expressed as;
M (X,Y) = {(x1+x2/2), (y1+y2)/2}
Given that M(-4, -3) and (x1, x2) = (-1, -2)
X = x1+x2/2
-4 = -1+x2/2
-8 = -1 + x2
x2 = -8 + 1
x2 = -7
SImilarly;
Y = y1+y2/2
-3 = -2+y2/2
-3*2 = -2+y2
-6 = -2 + y2
y2 = -6 + 2
y2 = -4
Hence the coordinate of B is (-7, -4)
No stealing points!!!!!
Answer:
8.74x10^5
Step-by-step explanation:
I think this is it..hope it helps
8.8*10^5 - 6000 = 874000 =8.74 x 10^5 in scientific notation.
How was y'all day. I hope it is good
Answer:
My day has been going great! And I hope your day is going great too! :)
Step-by-step explanation: You are a perfect human :>
can someone do my summer school work??
Answer:
no i can't do all of it, but i can help you do it
i just won't do it for you
I will give brainliest<3 help pleaseee
Answer:
24
Step-by-step explanation:
Answer: 24
Step-by-step explanation:
Helppppppppppppppppppppppp
$138.00
Step-by-step explanation:
Steven earns in 4 hours -$23.00
he earns in 6 hours-$34.50
there fore in 10 hours -23.00+34.50=$57.50
in 20 hours -57.50+57.50=$115
and in 4 hours-$23.00+115.00=138.00$
then he earn $138.00 one day
pls help me ???????????????????
Answer:
Hi♀️
Step-by-step explanation:
ΔMAN≅ΔNED
ΔRED≅ΔRGD
ΔLAN≅ΔLEI
ΔRKI≅ΔIYC
Hope it helps you!
use the circle to answer the questions
Answer:
Diameter: 10.8 cm
Circumference (in terms of π): 10.8π cm
Circumference (approximate): 33.91 cm
Step-by-step explanation:
Hi there!
We're given:
The radius (5.4 cm)1) Determine the diameter
[tex]d=2r[/tex]
Multiply the radius 5.4 cm by 2
5.4 × 2 = 10.8
Therefore, the diameter of the circle is 10.8 cm.
2) Determine the circumference of the circle
[tex]C=\pi d[/tex]
Plug in the diameter 10.8
[tex]C=10.8\pi[/tex]
Therefore, the circumference of the circle in terms of π is 10.8π cm.
3) Determine the approximate circumference of the circle
[tex]C=10.8\pi\\C=10.8(3.14)\\C=33.91[/tex]
Therefore, the approximate circumference of the circle is 33.91 cm.
I hope this helps!
Three golf balls are stored in a square prism container with a height of 6 inches and a base edge of 2
inches. The diameter of a golf ball is 1.68 inches.
Find the amount of space within the square prism not taken up by the golf balls.
6 in
2 in
2 in
O 21.5 in
O 7.4 in
O 16.6 in
O 31.4 in
Answer:
16.6 in
Step-by-step explanation:
Amount of space left = volume of prism - volume of 3 golf balls
volume of prism = base area x height
base area = area of a square = length² = 2² = 4
volume = 4 x 6 = 24
Volume of a sphere = 4/3 x pi x r^3
r = 1.68/2 = 0.84
4/3 x 3.14 x 0.84^3 = 2.48
volume of 3 balls = 2.48 x 3 =
Find the area of
A triangle with a base of 8 units and a height of 13 units
Answer:
52 units squared
Step-by-step explanation:
[tex]13 \: units\: \times 8 \: units \div 2[/tex]
Identify the lines that are perpendicular: Line 1: y=4 Line 2: y=1/5x-5 Line 3:y=8 Line 4:y+5=-5(x+1)
Greatest common factor for 63u^5, 45u^4, 27u
Answer:
9 u ^2
Step-by-step explanation:
Answer:
9u
Step-by-step explanation:
Greatest common factor for 63[tex]u^{5}[/tex], 45[tex]u^{4}[/tex], and 27u.
We can all divide them by 9, and that is the furthest we can get.
For the variables, the furthest we can get is u.
In conclusion, the greatest common factor for 63[tex]u^{5}[/tex], 45[tex]u^{4}[/tex], and 27u is 9u.
A penny is dropped from a point on a bridge 94 feet above the surface of the river. If the penny travels 250 feet straight down before it lands at the bottom of the river, find the depth of the river where the penny landed.
please provide with the strategies please!!
Answer:
156 ft
Step-by-step explanation:
the depth of the river =
250-94 = 156 ft
The triangles shown below are similar. Find the length of QS.
Answer: The value of QS is 8 cm.
Step-by-step explanation:
First calculating the side QT.
As per given figure:
ΔPQT ≈ ΔRST
[tex]\frac{PQ}{RS}=\frac{QT}{ST}[/tex]
Given:
PQ = 9 cm
RS = 3 cm
ST = 4 cm
Now putting all the given values in the above expression, we get:
[tex]\frac{PQ}{RS}=\frac{QT}{ST}\\\\\frac{9cm}{3cm}=\frac{QT}{4cm}\\\\QT=12cm[/tex]
Now calculating the value of QS.
QT = QS + ST
12 cm = QS + 4 cm
QS = 12 cm - 4 cm
QS = 8 cm
Thus, the value of QS is 8 cm.
plot triangle ABC with coordinates A(-4,5),B(-1,5),C(-1,1)
Answer:
:D
Step-by-step explanation:
Hay 31 personas en un café.Si hay 5 hombres más que mujeres,¿Cuantos hombres y mujeres hay en el café?
Answer: Hay 13 mujeres. (No hablo espanol.)
Combine like terms
1) 3y + 4y
2) -7( -4 - 2s)
3) 7f - 9f - 4
4) 9 + 7 + 6d + 2d
5) 7 + 9r + 3
6) -2(7 - 8s) - 4
7) q - 9q
8) -3( -2h + 6)
9) 3q + 9q - 4 + 2
10) 3 + 5(2d - 6)
Answer:
1.7y
2.-14s
3.-2f
4.23d
5.19r
6.-2s
7.-9q
8.24h
9.10q
10.23d
Step-by-step explanation:
I TRY MY BEST TO SOLVE IT
HOPE IT HELPS
CORRECT ME IF I AM WRONG
1. 7y
2. 28 + 14s
3. -2f - 4
4. 16 + 8d
5. 10 + 9r
6. -18+ 16s
7. -8q
8. 6h - 18
9. 12q - 2
10. 10d -27
Please help! Must get done ASAP!!!
^^
Answer:
No
No
Yes
Yes
Step-by-step explanation:
Try it.
Answer: 1st: No, 2nd: No, 3rd: Yes, 4th: Yes
Step-by-step explanation: You only flip the inequality when you divide a negative number on both sides. The only reason why you would divide would be to get the variable by itself - in this case the coefficient would need to be negative. That only applies to the third and 4th equations.