The fifth term of a geometric sequence is 32 and the eighth term is 4.
(a) Find the ratio. (2 marks)
(b) Find the first term. (2 marks)
(C) Find the sum of the first 50 terms of the sequence. (3 marks)
What is the first term?

Answers

Answer 1

Answer:

a. 1/2

b. 512

c. 1024

Step-by-step explanation:

The nth term of a geometric progression can be written as;

Tn = ar^n-1

where a is the first term, r is the common ratio and n is the term number

From the question;

Fifth term = ar^4 = 32

Eight term = ar^7 = 4

a. We want to find the common ratio

What to do here is that we can divide the 8th by the 5th term

ar^7/ar^4 = 4/32

r^3 = 1/8

r^3 = (1/2)^3

Thus r = 1/2

b. First term

we can make a substitution in any of the two given terms

Let’s use the fifth term

ar^4 = 32

a * (1/2)^4 = 32

a * 1/16 = 32

a = 16 * 32

a = 512

C. Sum of the first 50 terms

To calculate this, we use the sum of terms formula

Sn = a(1- r^n)/1-r

a = 512 , n = 50 and r = 1/2

Making the substitution;

Sn = 512(1-(1/2)^50)/1-1/2

Kindly note that (1/2)^50 will be infinitesimally small and will be close to zero

So we can approximate (1/2)^50 to be zero

Hence;

Sn = 512(1-0)/0.5

Sn = 512/0.5

Sn = 1024


Related Questions

cube root of 0.18125​

Answers

Answer:

0.005954345703125

Step-by-step explanation:

0.18125​^3 = 0.005954345703125

Hi! I need help on this one. Hope there's someone willing to help!!

Answers

2 of 5 is a 40% chance

40% * 40 = 16

He should expect to be stopped 16 times.

Is 4 - 4x and 4(1 - x) equivalent expressions? Why or why not?

Answers

Hey there!

ANSWER:

Yes

EXPLANATION:

Is 4 - 4x and 4(1 - x) equivalent expressions? Why or why not?

If you want to know whether they are equivalent, let's first find the value of both of them.

[tex]4-4x[/tex]

[tex]-4x+4[/tex]

[tex]4(1-x)[/tex]

Let's add parenthesis to 4 and (1-x) and add negative to x.

[tex](4)(1+-x)[/tex]

Now separate all with parenthesis.

[tex](4)(1)+(4)(-x)=4-4x\\-4x+4(ANSWER)[/tex]

Since both had the same value, they are equivalent.

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

Follow the guided instructions below to rotate the figure 90° clockwise about the
point (-1,1).
Click and drag to draw a line through the yellow center and the vertex on
the circle.
y
10
9
8
7
6
5
3
2
0 1
-1
3
4
-5 4 3
5
6
7
8
9
10
-10-9-8
-3
-4
-5
-6

Answers

Answer:

1111111111111111

Step-by-step explanation:

222222222222

help me i have no clue

Answers

Answer:

It seems like D if I eyeball it.

the shower should be d. i hope this helps.

You pick one card from a standard deck of 52 cards. What is the probability that the card will be a two?

Answers

Answer:

4 out of 52 or simplified 2 out of 26

Step-by-step explanation:

There are 4 suites of cards, spades, hearts, clubs, diamonds and there is one card for two in each suite, so we therefore know that the probability of picking a two out of a 52 card deck will be four out of 52 or the simplified answer would be 2 out of 26. Hope this helps, have a great day!

Emily owns 10.2 shares of stock in a company. On Friday, the stock dropped by $1.35/share. What was the total change in value of Emily’s stock? −$13.77 −$7.56 +$7.56 +$13.77

Answers

Answer:

-$13.77

Step-by-step explanation:

Is -5 a integer or rational or irrational?

Answers

Answer:

irrational

Step-by-step explanation:

Answer:

It's rational because it isn't a decimal with no end. To simplify it even more, it is an integer.

Step-by-step explanation:

Convert this rational number
to its decimal form and round
to the nearest thousandth.
7/8

Answers

Answer:

.875

Step-by-step explanation:

Here are two five-pointed stars. A student said, “Both figures A and B are polygons. They are both composed of line segments and are two-dimensional. Neither have curves.” Do you agree with the statement? Explain your reasoning.

Answers

Answer:A

Step-by-step explanation:

Bcnitsreksbeux

2+2x + x^2 +XY

What would be the answer to this question simplified

Answers

Hey there!

ANSWER: [tex]x^2+xy+2x+2[/tex]EXPLANATION:

[tex]2+2x+x^2+x*y[/tex]

To solve, you will need to simplify.

[tex]x^2+xy+2x+2[/tex]

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

if α,β are the roots of the equation x^{2}-3x+2=0 form an equation whose roots are (α+β)² & (α-β)²

Answers

Solution:-

Let's find roots of x² - 3x + 2

=> x² - 3x + 2 = 0.

=> x² - x - 2x + 2 = 0.

=> x ( x - 1 ) -2 ( x - 1) = 0.

=> ( x - 1 ) ( x - 2 ) = 0.

=> x = 2, 1.

Now

( a + ß )² = (2+1)²=3²=9( a - ß )² = ( 2 - 1 )² = 1² = 1.

So , equⁿ would be ,

=> x² - ( 9 + 1)x + 9×1=0.

=> x² - 10x + 9=0.

A conditional statement can be written as "If hypothesis, then conclusion". How can "your phone is set to vibrate so it will not disturb others" be written as a conditional statement?

Answers

Answer:

If your phone is set on vibrate, then it will not disturb others.

Step-by-step explanation:

It's an if then statement.

What is the domain of the given relation?
{(0, – 1), (2, - 3), (3, - 2)}
A
{0, 2, 3}
B
{ -3, - 2, - 1}
C
{ - 3, – 2,3}
D
{ - 1,0,2}

Answers

Answer:

Option (A) : {0,2,3} is the domain

f(x) = -2x, g(x)= -2x-1

Answers

Answer:

I graphed the two points on a graph in the attachment! Hope this helps! :)

Step-by-step explanation:

The candle maker makes a total of 454545 orange candles. This is 30\%30%30, percent of all the candles she made this week. How many candles did the candle maker make this week?

Answers

Answer:

150 candles

Step-by-step explanation:

plz help!!!! (click on the pic)

Answers

Answer:

x^2+8x

Step-by-step explanation:

instructions included above :)

Answer....

[tex] \boxed{ {x}^{2} + 8x}[/tex]

[tex] \boxed {\tt{Step-by-step \: explanation:-}}[/tex]

(6x²+10x-1)+(-5x²-2x+1)

=6x²+10x-1-5x²-2x+1

=6x²-5x²+10x-2x-1+1

=x²+8x

Brad's checking account starts off with a balance of $126.50. Throughout the week, Brad pays a bill for $87.21, and pays $5.64 for breakfast. He deposits $15.00 but then pays another bill for $55.25. At the end of the week, he gets a notice from the bank that he has a negative balance. How much does Brad need to deposit into his account to get to a $0 balance?

Answers

Answer:

$6.6

Step-by-step explanation:

Let's find out what his balance is after those transactions.

Initial balance: 126.50

After bill:

126.50 - 87.21 = 39.29

After breakfast:

39.29 - 5.64 = 33.65

After deposit (we're adding money now!):

33.65 + 15 = 48.65

After 2nd bill:

48.65 - 55.25 = -6.6

We find that his balance is negative $6.6. Thus, to get to $0, he needs to deposit an additional $6.6.

Answer: $6.6

Encuentren dos números cuyo cociente sea -1 y que la resta del primero menos el segundo sea -3/2

Answers

Answer:

[tex]\dfrac{3}{4}\ \text{and}\ \dfrac{-3}{4}[/tex]

Step-by-step explanation:

Find two numbers whose quotient is -1 and the subtraction of the first minus the second is -3/2

Let two numbers are x and y. When they are divided the quotient is -1. So,

[tex]\dfrac{x}{y}=-1[/tex]

It can also be written as :

x = -y ....(1)

The subtraction of first minus the second is -3/2 .

[tex]x-y=\dfrac{-3}{2}\ .....(2)[/tex]

Use equation (1) in (2),

[tex]-y-y=\dfrac{-3}{2}\\\\-2y=\dfrac{-3}{2}\\\\y=\dfrac{3}{4}[/tex]

From equation (1) : [tex]x=\dfrac{-3}{4}[/tex]

Hence, two numbers are [tex]\dfrac{3}{4}\ \text{and}\ \dfrac{-3}{4}[/tex].

So I need help with this because I had did it but the teacher said to redo it but I forgot the answers,
Please help !

Answers

i’ll answer the first question, what’s 3 plus 13? 16 that’s your answer


What is m 50
65
140
155

Answers

Answer:

65 degrees.

Step-by-step explanation:

Since angle JLG is 115 degrees, andgle JLH must be 65 because the two angles are supplementary, which means they add up to 180 degrees.

what is the answer 2(3x-4)+3(7-12x)

Answers

Answer:

-30x+13

Step-by-step explanation:

6x-8 + 21 - 36x

-30x+13

Solve it
it's easy
take as much time you need☺️​

Answers

hope it helps......hehhehehe

Step-by-step explanation:

101^2= [100+1]^2

[100]^2 +1^2+2×100×1

=10000+1+200

=10201

HOPE IT HELP.......

A store sells candles.
• The retail price was a 45% markup
over the manufacturer price.
• A month later, the store reduced the
retail price of the candles by 20
percent.
What percent markup is the new retail
price over the manufacturer price?

Answers

Answer:

25%

Step-by-step explanation:

If you start at 45% and it reduces by 20% you are just doing 45-20 which equals 25. (Please let me know if im wrong)

16 percent markup is the new retail price over the manufacturer price.

Here,

A store sells candles.

Retail price will be 45% marked-up

A month later, store reduced the retail price of the candles by 20%.

We have to find the percent markup.

What is the percentage?

The percentage is the value per hundred.

Now,

Consider the manufacturer price = 100x

Retail price will be 45% marked-up

Hence,  100x+45% of 100x = 145x

Reduced retail price of the ladder after one month = 145x-145x*20/100

Reduced retail price of the ladder after one month = 116x

Percentage markup of the reduced retail price over the manufacturer price will be:

={(reduced retail price - manufacturer price)/manufacturer price} *100

=[ (116x-100x)/100x ] *100 = 16%

Hence, 16 percent markup is the new retail price over the manufacturer price.

Learn more about the Percentage visit:

https://brainly.com/question/19247356

#SPJ2

Find 2 equivalent fractions to 4/6

Answers

The two answers are:
8/12
2/3
4 and 6 is 2, so 4/6 is equivalent fraction of 2/3

Plane zwv and plane tuv intersect at

Answers

Answer:

Option (1)

Step-by-step explanation:

Planes ZWV (shaded side) and plane TUV (Top of the box) are the two sides of the given cube or box in the picture attached,

Common edge of the given planes is side SV.

Common edge or the line where two planes meet is the line of intersection of two planes.

Therefore, line SV will be the line of intersection of the given planes.

Option (1) will be he answer.

The coordinates of points A and B are A(4, -2) and B(12, 10). What are the coordinates of the point that is 1/4 of the way from A to B?

Answers

Answer:

Step-by-step explanation:

(4 + 12)/4 = 16/4 = 4

(-2 + 10)/2= 8/4 = 2

(4, 2) is 1/4 of the way from A to B

The coordinates of the point that is 1/4 of the way from A to B is (28/5, 2/5) if the coordinates of points A and B are A(4, -2) and B(12, 10).

What is an ordered double?

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

The coordinates of points A and B are A(4, -2) and B(12, 10)

The coordinates of the point that is 1/4 of the way from A to B

The above statement means that the line segment AB is divided in the ratio of 1:4 internally.

Using the section formula:

Let C be the new coordinate point:

C(x) = [1(12) + 4(4)]/(1+4)

C(x) = 28/5

C(y) = [1(10) + 4(-2)]/(1+4)

C(y) = 2/5

Thus, the coordinate of the point that is 1/4 of the way from A to B is (28/5, 2/5) if the coordinates of points A and B are A(4, -2) and B(12, 10).

Learn more about the ordered double here:

brainly.com/question/10757890

#SPJ2

Guys I really need help!
The general equation for the geometric sequence -1, -2, -4, ... is a n = -1 · 2 n - 1 .


TrueFalse

Answers

Answer: false

Step-by-step explanation:

Answer:

Yes absolutely true i took the lesson

Step-by-step explanation:

what is the value of x?

Answers

Answer: 4

Step-by-step explanation:

subtract 10 from 18 , thats 8 then divide 8 by 2 and get 4.


Which are the roots of the quadratic function f(b) = 62-75? Select two options,
b=53
b= -573
Ob=35
b = -315
b = 256

Answers

Answer:b=573

Step-by-step explanation:

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