Given:
The sum of two terms of GP is 6 and that of first four terms is [tex]\dfrac{15}{2}.[/tex]
To find:
The sum of first six terms.
Solution:
We have,
[tex]S_2=6[/tex]
[tex]S_4=\dfrac{15}{2}[/tex]
Sum of first n terms of a GP is
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex] ...(i)
Putting n=2, we get
[tex]S_2=\dfrac{a(1-r^2)}{1-r}[/tex]
[tex]6=\dfrac{a(1-r)(1+r)}{1-r}[/tex]
[tex]6=a(1+r)[/tex] ...(ii)
Putting n=4, we get
[tex]S_4=\dfrac{a(1-r^4)}{1-r}[/tex]
[tex]\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}[/tex]
[tex]\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}[/tex]
[tex]\dfrac{15}{2}=6(1+r^2)[/tex] (Using (ii))
Divide both sides by 6.
[tex]\dfrac{15}{12}=(1+r^2)[/tex]
[tex]\dfrac{5}{4}-1=r^2[/tex]
[tex]\dfrac{5-4}{4}=r^2[/tex]
[tex]\dfrac{1}{4}=r^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{\dfrac{1}{4}}=r[/tex]
[tex]\pm \dfrac{1}{2}=r[/tex]
[tex]\pm 0.5=r[/tex]
Case 1: If r is positive, then using (ii) we get
[tex]6=a(1+0.5)[/tex]
[tex]6=a(1.5)[/tex]
[tex]\dfrac{6}{1.5}=a[/tex]
[tex]4=a[/tex]
The sum of first 6 terms is
[tex]S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}[/tex]
[tex]S_6=\dfrac{4(1-0.015625)}{0.5}[/tex]
[tex]S_6=8(0.984375)[/tex]
[tex]S_6=7.875[/tex]
Case 2: If r is negative, then using (ii) we get
[tex]6=a(1-0.5)[/tex]
[tex]6=a(0.5)[/tex]
[tex]\dfrac{6}{0.5}=a[/tex]
[tex]12=a[/tex]
The sum of first 6 terms is
[tex]S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}[/tex]
[tex]S_6=\dfrac{12(1-0.015625)}{1.5}[/tex]
[tex]S_6=8(0.984375)[/tex]
[tex]S_6=7.875[/tex]
Therefore, the sum of the first six terms is 7.875.
The difference between two numbers is 2.5 . The product of those two numbers is 21. Provide the 2 equations needed to solve the application separated by a comma and NO SPACES.
Answer:
x-y=2.5,xy=21
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
One of the numbers is x.
The other number is y.
The difference between two numbers is 2.5
This means that x - y = 2.5
The product of those two numbers is 21.
This means that xy = 21.
So the two equations are: x-y=2.5,xy=21
solve the inequality -1/3h_<7
Answer:
The solution to the given inequality
[tex]h\geq \frac{-1}{21}[/tex]
Step-by-step explanation:
Given inequality
[tex]\frac{-1}{3h} \leq 7[/tex]
⇒ -1≤ 7× 3h
⇒ -1 ≤ 21 h
⇒ 21 h ≥ -1
⇒ [tex]h\geq \frac{-1}{21}[/tex]
what is the 28% of 349 multiplied by 7
Answer:
Step-by-step explanation:
E X P L A N A T I O NAnswer:
The answer is 684.04
Step-by-step explanation:
Sansa solved the equation 1/2(8x-6)=x+9
Answer:
x=4
Step-by-step explanation:
;)
Please help and explain
True or False: The magnitude of a resultant vector will always be larger than individual vectors that are both in the first quadrant
Answer:true
Step-by-step explanation:
Find the slope of the line that passes through the points (2,8) and (6,8).
Answer:
8-8/6-2
0/4
answer is 0
y=0x+c
8=0(2)+c
8=0+c
8=c
y=0x+8 i thinkkk
Step-by-step explanation:
Answer:
8-8/6-2
0/4
answer is 0
y=0x+c
8=0(2)+c
8=0+c
8=c
y=0x+8
Step-by-step explanation:
Integrate [tex]e^{4x}\sqrt{1+e^{2x} } dx[/tex] please show work so i can learn
Answer:
the picture is attachedand sorry I can't explain you much about itWhich is the correct algebraic expression for the phrase: 13 times the cost of one ticket and an $8 soda
Answer:
13 X 8
Step-by-step explanation:
Two students on roller skates stand face-toface, then push each other away. Which student will always have the fastest speed
Answer:
The student with lower weight will move faster than the one with higher weight.
Step-by-step explanation:
The students are on roller skates and it is assumed that their wheels are identical. They are on a frictionless flat horizontal ground. According to Newton's Law F=ma
Mass of student 1 is 97 kg
Mass of student 2 is 61 kg
The force magnitude is assumed to be equal and acceleration is same. The student with higher weight will have lesser force exerted than the student with lighter weight.
✨PLS HELP ILL GIVE BRAIN ALIST ✨Jared has $476.24
saved. Which equation
can be used to
determine
m, the
amount of money he
still needs to earn to
reach his goal of saving
$500.00?
Answer:
the 1st one
Step-by-step explanation:
he's savings estimate to 476.24 and to reach his goal of 500 usd he has to add a certain amount of money, portrayed by m
Royce Bernstein’s group medical insurance coverage costs $5,480 a year. His employer pays 65% of the cost. What is the amount of the deduction each month from his paycheck medical insurance
Can someone answer this question for me
Jill and Kyle get paid per project. Jill is paid a project fee of $35 plus $8 per hour. Kyle is paid a project fee of $20 plus $16 per hour. Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.
Answer:
The company will pay $43 project fee and $24 an hour.
Step-by-step explanation:
25 + 10h +18 + 14h
= 25+ 18 + 10h + 14h
=43 + 24h
Witch one is a function?
This shows a list of points where the x coordinate does not repeat. This means that any given x input leads to exactly one y output.
Something like choice A has x = 6 repeated; showing that x = 6 leads to both y = 11 and y = -9 at the same time. So this is why choice A is not a function. Choice B has x = 1 repeat, so it's not a function either. Choice C has x = 19 repeated, so it's not a function.
As a visual tool, you can use the vertical line test to check each set of points. If you are able to draw a single vertical line through more than one point on the graph, then it is not a function.
Answer: A
Step-by-step explanation: I hope I help you if it was wrong I'm sorry
Fill in the missing
number to make the
number sentence
true.
| 148 +___= 179
Answer: 31
Step-by-step explanation:
179 - 148 = 31
The answer is 31.
Step-by-step explanation:
179 -- 148 = 31.
148 + 31 = 179
Which number line diagram represents the solution to the inequality?
A
B
C
D
Answer:
C
Step-by-step explanation:
mary ann spent $26.85 total on two new toys. She had a coupon for 1.00 off her total purchase and spend 1.75 on sales tax. Each toy cost the same amount how much did each toy cost?
Answer: $13.80
Step-by-step explanation:
Mary ann spent $26.85 total on two new toys but had a coupon for $1.00 off her total purchase. Therefore, we subtract $1.00 from $26.85. This will be:
= $26.85 - $1.00
= $25.85
Shw then spend $1.75 on sales tax. Total coat will now be:
= $25.85 + $1.75
= $27.60
Since each toy coat same amount, therefore each toy will cost:
= $27.60 / 2
= $13.80
HELP!!! LOTS OF POINTS
A bakery did a survey among 100 customers to find their food preference . The customers were asked about their preferences for cupcakes or brownies. Out of the total 72 people who liked cupcakes, 37 also liked brownies. There were 59 people who liked brownies.
Part A. Summarize the data by writing the values that the letters A to I in the table below represents
PART B. What percentage of the survey respondents did not like cupcakes or brownies ?
PART C . Do the survey results reveal a greater dislike for brownies or cupcakes? Justify your answer
(I added a picture down below)
Answer:
Answer:
put 37, 22,59,35,6,41,72,28,100 in chart < That is for the ppl who cant click on the brainly site but it still shows alitttle
For the ppl who can click on brainly:
Part A:
Like Cupcakes
Do Not Like Cupcakes
Total
Like Brownies
37
22
59
Do Not Like Brownies
35
6
41
Total
72
28
100
Part b: 6
Part c: You really have to figure out how to word this 37- 72=35 35-41=6
hope it helps
The diagram shows a piece of cheese in the shape of the triangular prism.Work out the area of the cling film needed to cover the cheese
Answer:
488.4 cm²
Step-by-step explanation:
Area of cling film needed = surface area of the triangular prism = 2(B.A) + P×H
Where,
B.A = triangular base area = ½*base*height
height = 10.5 cm
base = √(13.7² - 10.5²) = √77.44 = 8.8 cm
B.A = ½*8.8*10.5 = 46.2 cm²
P = perimeter of the triangular base = 10.5 + 13.7 + 8.8 = 33
H = height of prism = 12 cm
Surface area of triangular prism = 2(46.2) + 33*12
= 92.4 + 396
= 488.4 cm²
Select the correct symbol
Answer:
The answer is <
Evaluate.
1 to the power of 3
Answer:
3
Step-by-step explanation:
ndnsjsjwnanaksodbsjcif
13 14
x
7 11
What is 13/7 times 14/11 equal
Answer:
(2 × 7 × 13) / (7 × 11) =
((2 × 7 × 13) ÷ 7) / ((7 × 11) ÷ 7) =
(2 × 7 ÷ 7 × 13)/(7 ÷ 7 × 11) =
(2 × 1 × 13)/(1 × 11) =
(2 × 13)/11 =
26/11;
Step-by-step explanation:
Answer:
182/77 is the normal answer
the answer is 26/11 in simplest form
George buys pizza. He eats 3/8 of pizza for lunch and 1/4 of the pizza for dinner
Answer:
Step-by-step explanation:
To find the amount he ate we just add the fractions:
3/8 +1/2 = 7/8 or 0.875
HOPE THIS HELPS!
HAVE A GR8 DAY ;-)
Help pls I need it before 11:59
Answer:
5/6
Step-by-step explanation:
probability of rolling a 5 on a die=1/6
P of not rolling a 5 = 1-1/6= 5/6
Find mZVUT if IZAUT = 88
and mZVUA = 55°.
T
U
V
9514 1404 393
Answer:
143°
Step-by-step explanation:
Angle VUT is the sum of the angles into which it is divided.
∠VUT = ∠VUA +∠AUT
∠VUT = 55° +88°
∠VUT = 143°
Helpp
(Show ur work please)
This is law of cosine
Answer:
13.3
Step-by-step explanation:
[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]
[tex] a^2 = 8^2 + 18^2 - 2(8)(18) \cos 43^\circ [/tex]
[tex] a^2 = 64 + 324 - 288(0.73135) [/tex]
[tex] a^2 = 388 - 210.6299 [/tex]
[tex] a^2 = 177.370 [/tex]
[tex] a = \sqrt{177.370} [/tex]
[tex] a = 13.318 [/tex]
Answer: 13.3
Four friends are training for long races. Eduardo ran 5.123 miles, Kandis ran 6.34 miles, Khaliyah ran 7.1 miles, and Moises ran 8 miles. b: Khaliyah ran how much further than Eduardo?
Answer:
1.977 miles
Step-by-step explanation:
Focus on how many miles Khaliyah and Eduardo are training.
Khaliyah = 7.100 miles
Eduardo = 5.123 miles
Difference = 7.100 - 5.123 = 1.977
HELPPPPPPPP ASAP HELPPPPP PLSSSSSSSSSS
b) Simplify (4ab^2)^3
Answer:
[tex]64a^{3} b^{6}[/tex]
Step-by-step explanation:
[tex](4ab^2)^3[/tex]
=> [tex]4^{3} a^{3} b^{6}[/tex]
=> [tex](4 \times 4 \times 4) a^{3} b^{6}[/tex]
=> [tex]64a^{3} b^{6}[/tex]
PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!! WILL GET BRAINLEST IF CORRECT!!!!!!!!!!!!!!!!!!!!!!
Answer: x=40
Step-by-step explanation:
Answer:
X equals 40.
Step-by-step explanation:
since the other side is 120 degrees then the side opposed to it would also be 120. in case you're wondering what the other two sides are, they are both 60.