Find the sum of the first five terms using the geometric series formula for the sequence 1/2, -1,2,-4…

Answers

Answer 1

The sum of the first five terms is 11/2

How to determine the sum?

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

[tex]S_n = a\frac{1 - r^n}{1 - r}[/tex]

This gives

[tex]S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}[/tex]

Evaluate

[tex]S_n = \frac{1}{2} * \frac{33)}{3}[/tex]

Evaluate

[tex]S_n =\frac{11}{2}[/tex]

Hence, the sum of the first five terms is 11/2

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Related Questions

Sixty less than ten times ten

Answers

Answer:

40

Step-by-step explanation:

10x10=100

100-60=40

Hope this helps! :)

sum of two numbers is -17. Their difference is 41. Find the numbers

Answers

Answer:

[tex]Suppose~the~two~numbers~are~x~and~y.\\From~the~first~condition,\\x+y=-17...........(1)\\From~the~second~condition,\\x-y=41.............(2)\\Adding~eq^n(1)~and~eq^n(2),~we~get,\\x+y+x-y=-17+41\\or, 2x = 24\\or, x=12\\Substituting~x=12~in~eq^n(2),\\y = -17-x = -17-12 = -29[/tex]

[tex]So,~the~two~numbers~are~12~and~-29.[/tex]

Can someone please help me with my homework

Answers

Answer:

Do not use, there's still one more piece of the puzzle missing.

X =

Step-by-step explanation:

Lets look everything over and compare the corresponding parts of the 2 triangles.

One side of each is shared between the two triangles.

Another side of each triangle is 13 on each triangle.

The included angle of one triangle is 80 degrees and the other is 110 degrees.

simplify the following expression, show all work you did to get the results​

Answers

Answer:

(sqrt(7))/3 or decimal 0.8819171036881968635005385845464201419034197276941500601227781530...

Step-by-step explanation:

Simplify the following:

(sqrt(14))/(sqrt(18))

Hint: | Simplify radicals.

sqrt(18) = sqrt(2×3^2) = 3 sqrt(2):

(sqrt(14))/(3 sqrt(2))

Hint: | Multiply numerator and denominator of (sqrt(14))/(3 sqrt(2)) by sqrt(2).

Rationalize the denominator. (sqrt(14))/(3 sqrt(2)) = (sqrt(14))/(3 sqrt(2))×(sqrt(2))/(sqrt(2)) = (sqrt(14) sqrt(2))/(3×2):

(sqrt(14) sqrt(2))/(3×2)

Hint: | Multiply 3 and 2 together.

3×2 = 6:

(sqrt(14) sqrt(2))/6

Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(14) sqrt(2).

sqrt(14) sqrt(2) = sqrt(14×2):

(sqrt(14×2))/6

Hint: | Multiply 14 and 2 together.

14×2 = 28:

(sqrt(28))/6

Hint: | Simplify radicals.

sqrt(28) = sqrt(2^2×7) = 2 sqrt(7):

(2 sqrt(7))/6

Hint: | In (2 sqrt(7))/6, divide 6 in the denominator by 2 in the numerator.

2/6 = 2/(2×3) = 1/3:

Answer:  (sqrt(7))/3

If m∠AEB = 88°, find m∠AED

Answers

Answer:

fjruehbrehjfg

Step-by-step explanation:

h3efhrifhe

ABCD is a parallelogram. If m/CDA = 63, then m/ABC = ? . The diagram is not to scale

Answers

it’s 63 because the sides are equal on both sides

At a summer camp, 5 out of 12 campers are signed up for horseback riding. If there are 432 campers at the camp, how many are signed up for horseback riding?

Answers

Answer:

The answer is 180.

Step-by-step explanation:

(5/12) x 432 = 180

Answer:

I just need points

Step-by-step explanation:

b. Solve for x, given the
MZ2 = 9x + 6

Answers

Answer:

Step-by-step explanation:

hello :

9x+6 =60

9x+6-60 =60-60

9x -54 =0

9x -54+54 =+54

9x=54

x = 54/9

x= 6°

З
3
2
5
х1
х9
9
З
х3
. . . . . .
7
5
2
1
3 г.)
Х
x 9
x 9
# F​

Answers

Answer:

bu ney ben anlamadım gerçek

تيتيتيوييننينينينقنقنبنبنبنبنبنخل

CAN SOMEONE PLEASE HELP ME!!!!!!!!!

Answers

Answer:

12(m +1) > 18m - 3

12m + 12 > 18m - 3

12+3 > 18m - 12m

15 > 6 m.

m < 15/6

m < 2.5

4th option is correct.

Answer:

{m| m < 2.5}

Step-by-step explanation:

m < 2 1/2,m < 2.5 , m ∑ [-∞, 5/2]

hope that helped!

Evaluate the expression when b=-7 and c=2.
b-6c
X 5
?

Answers

Answer:

-19

Step-by-step explanation:

-7 - 6(2) =

-7 - 12 =

-19

Factor by grouping.
30y + 3h + 10vr + hr

Answers

Answer:

30y+hr+10rv+3h

Step-by-step explanation:

Hope this helps

I decided to give you 2 answers because there’s no way you can continue factoring unless the “30y” was “30v”. So, I did it both ways for you, just in case! ;)

Simplify (3^z)^6 in exponent notation

Answers

Answer:

3^6z

Step-by-step explanation:

you multiply 6 and z since they are exponets and one is in a (

Answer:

3 to the power of 6z of 3^6z

Step-by-step explanation:

Can someone please help me

Answers

Answer:

the answer is d

Step-by-step explanation:

Answer:

It's either A or D but I don't know because I don't know where the 1 starts.

Step-by-step explanation:

Sam has two coupons for a bicycle. coupon A: $20 rebate on a $95 bicycle. coupon B: 25% off a $95 bicycle. choose the coupon that gives the lower price. then fill in the blank​

Answers

Answer:

B

Step-by-step explanation:

on a nice day there are 90% of children playing outside during recess. if there are 150 children how many of them are playing outside

Answers

Answer:

150.9  ?

Step-by-step explanation:

Miguel withdrew $20 per week from his bank account for 4 weeks. Which expression shows the change in his account balance?
A. -20+4
B. -20-4
C. -20x4
D. -20 ÷4

Answers

Answer:

c

Step-by-step explanation:

The expression that shows the change in Miguel's account balance is -20×4. Thus, option (C) is correct.

Given, Miguel withdrew $20 per week from his bank account for 4 weeks.

Since he withdrew money, the change in his account balance would be negative.

The expression -20 represents the amount he withdrew each week, and the -4 represents the number of weeks.

Multiplying 4 with the initial balance of -20 gives us the change in his account balance.

Therefore, the expression -20×4 correctly represents the change in Miguel's account balance.

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what THE fRiCk is 3 3/4 as a fraction Bigger than 1

Answers

Answer:

I am pretty sure that it is.

Step-by-step explanation:

Isn't 3 bigger than 1

Well i hope this helps

Have a great day!!!!!!!

Three is bigger than one so yes it is

Find the area of the triangle.
3 yd!
2.
12 yd
The area of the triangle is
square yards.

Answers

Area is 18 yards hoped this help

Graph the equation using slope-intercept form (y=mx +b)
-3x + y = -2

Answers

both x-axis in the graph is before 5 or -5

SLOPE-INTERCEPT: y=3x-2

Answer
-3x+y=-2
y=3x-2

A group of 1,254 people are going on a boat tour. If each boat holds 8 people, how many boats will they need?

Answers

Answer:

Step-by-step explanation:

1254p(b/(8p))=156.75b

The number of boats must be an integer because you can’t have a fraction of a boat so

b=157

What are verbs? Example ​

Answers

Answer:

Hi! Hope this helps!

Step-by-step explanation:

A verb is used to describe actions.

Example: I JUMPED over the rock. In this sentence the verb is JUMPED

a ver

Step-by-step explanation:

a verb is a word used to describe an action , state , occurrence and forming the main part of a predicate of a sentence

I need help on this and pls I actually do so dont put wrong answers or that you need points pls dont :)

Answers

Answer:

Equation: 120=66+2m

Step-by-step explanation:

120=66+2m

120-66=54

54/2=27

m=27

Can somebody please help me and how do you do this step by step and I need the formula for this please.

Answers

radius of ½ circle = d : 2

= 6in : 2 = 3in

Total area = Rectangle area + ½Circle area + Triangle area

= (w) + ½(π×r²) + (½×b×h)

= (10×6) + ½(π×3²) + (½ × (14-10) × 6)

= 60 + 14.14 + 12 = 86.14in

Answer : 86.14in

See the bold one in line 2 of total area, thats the formula of all shape.


Can someone help me please?

Answers

Given:

A line segment AB.

A point is [tex]\dfrac{3}{10}[/tex] of the way from A to B.

To find:

The coordinates of that point.

Solution:

Section formula: If a point divide a line segment in m:n, then

[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

From the given figure, it is clear that the two end points of the line segment are A(-4,-5) and B(12,4).

Let the unknown point be P. The point is [tex]\dfrac{3}{10}[/tex] of the way from A to B. It means,

[tex]\dfrac{AP}{AB}=\dfrac{3}{10}[/tex]

Let AP and AB are 3x and 10x, then

[tex]\dfrac{AP}{PB}=\dfrac{AP}{AB-AP}[/tex]

[tex]\dfrac{AP}{PB}=\dfrac{3x}{10x-3x}[/tex]

[tex]\dfrac{AP}{PB}=\dfrac{3x}{7x}[/tex]

[tex]\dfrac{AP}{PB}=\dfrac{3}{7}[/tex]

It means, point P divided the line segment in 3:7.

Using section formula, we get

[tex]P=\left(\dfrac{3(12)+7(-4)}{3+7},\dfrac{3(4)+7(-5)}{3+7}\right)[/tex]

[tex]P=\left(\dfrac{36-28}{10},\dfrac{12-35}{10}\right)[/tex]

[tex]P=\left(\dfrac{8}{10},\dfrac{-23}{10}\right)[/tex]

[tex]P=\left(0.8,-2.3\right)[/tex]

Therefore, the coordinates of the required point are (0.8, -2.3).

21 divided by 4,857 with remainder

Answers

The answer is 231 R6

hi everyone i know all the ansers but i wanna help people too 9x8 2x12

Answers

First answer is 72 and second is 24

An item that was selling for $82.00 is reduced to $60.00. Find the percent decrease in price. Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

Amount of decrease = 82-60 = 22

percentage decrease = 22/82 ≅ 0.268 = 26.8%

Solve the Equation
-8.3 = d+4.7

Answers

Answer:

d = -13

Step-by-step explanation:

-8.3 = d + 4.7

-8.3 - 4.7 = d

-13 = d

-8.3=d+4.7

What you want to do is flip the equation like this:

d+4.7=-8.3

The next step is to subtract 4.7 from both sides of the equation:

d+4.7=-8.3

-4.7 (both sides)

this equals to d=-13

Your final answer is d=-13 (negative 13).

Hope this helps!!

Find the missing lengths or missing angles

Answers

Answer:

18

Step-by-step explanation:

its an isoceles triangle, the two sides (NP and Q) are equal

Answer:

18

Step-by-step explanation:

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