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.
insert one pair of brackets only to make the following statement correct 6 +5*10-8=16
Answer:
6+5*(10-8)=16
Step-by-step explanation:
Using BODMAS multiplication takes precedence over addition and subtraction so as it stands it would be calculated as 6 + (5*10) - 8. To get the answer 16 it would be 6 + 5(10 - 8) Solving the brackets first, this gives 6 + (5*2) which gives 16.
Find the two solutions to the equation below.
(x – 3)(x − 2) = 0
Anyone know how to do it
Answer:
You have two brackets..divide them as
x-3=0 and x-2=0
so x=3, x=2
The solutions to the equation ( x – 3 )( x − 2 ) = 0 using factors equal to zero are x = 3 and x = 2.
To find the solutions to the equation ( x – 3 )( x − 2 ) = 0, we set each factor equal to zero and solve for x. This is because the product of two factors is equal to zero only if at least one of the factors is zero.
Setting ( x – 3 ) = 0:
x – 3 = 0
x = 3
Setting ( x − 2 ) = 0:
x − 2 = 0
x = 2
Therefore, the solutions to the equation ( x – 3 )( x − 2 ) = 0 are x = 3 and x = 2.
To know more about equation click here :
https://brainly.com/question/28741857
#SPJ2
What is equivalent to 16/18
Answer: 16/18 reduced is 89 :D
Step-by-step explanation:
Answer:
8/9
32/36
64/72
etc
Step-by-step explanation:
Jaiden walked 2 1/2 miles to his friend's house. Miya had to walk 4 3/8 miles to the same friend's house. How many times the length of
Jaiden's walk was Miya's walk?
Answer:
Jaidens walk was 2 4/8 miles long and
Miyas walk was 4 3/8 miles long so
Miyas walk was 2 1/8 mile longer than Jaidens
Step-by-step explanation:
Coupd someone help me with this? (picture)
Answer:
2x3 = 6
6x14 = ...
Step-by-step explanation:
All the solutions with a + in them are not applicable to this multiplication
What is the distance between the points (21 , 11) and (4 , 11) in the coordinate plane?
Many newspapers carry a certain puzzle in which the reader must unscramble to form words. how many ways can the letters LEZBA be arranged?
Manny bought a car for $32,985. Five years later, the car was worth $19,500. Find the percent of change in the value of the car.
Answer:
is 40.9
Step-by-step explanation:
The percent of change in the value of the car is 40.88%
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, Manny bought a car for $32,985. Five years later, the car was worth $19,500.
Percentage change = (32985-19500)/32985*100 = 40.88%
Hence, The percent of change in the value of the car is 40.88%
For more references on percentage, click;
https://brainly.com/question/29306119
#SPJ2
The function f is defined by f(x) = 2x^2–5.
Find f (5x).
Answer: f(5x)=(50x^2)-5
Step-by-step explanation:
f(5x)=2(5x)^2-5
=2(25x^2)-5
=50x^2-5
Learn more about function here:
https://brainly.com/question/2253924
#SPJ2
Jill's mother is 37 years old. Her age is three years more than twice Jill's age. What is
Jill's age?
what's lateral surface area of a pyramid?
Step-by-step explanation:
The lateral surface area of a pyramid is the area of each side of a right rectangular prism. The lateral area of a right pyramid can be calculated by multiplying half of the perimeter of the base by the slant height. The lateral surface area can also be found using this equation (see attachment.)
Help me on this question please
Answer:
j = h + 9
Step-by-step explanation:
To go from 3 to 12, add 9 to 3. Add 9 to 4 to get 13. Add 9 to 5 to get 14.
In each case, add 9 to the value of h to get j.
j = h + 9
Answer:
it's the first one j=h+9
Step-by-step explanation:
as you can see the pattern you will look at all the answer choices and eliminate them one by one since it is the first answer you will be adding the numbers from the input by 9 and it will give you the output as you can see the other answers they are either multiplying by 9 or you just can't add them with the equation.
What is the result when 6x3 + 11x2 + 9x + 2 is divided by 3x + 1?
Answer:
(6x^(3)+11x^(2)-19x+5)-:-(3x-2)
Step-by-step explanation:[tex]63+112+32+1[/tex]
for some reason it showed that but yeah hope this helps!
4.(06.02 MC)
The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB In slope-Intercept form that contains point (3,-2). (4 points)
O y = 2x + 4
O y = 2x - 8
Answer:
The equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:
y = 2x- 8Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
m is the slopeb is the y-interceptGiven the equation of a line
y = 2x + 4
comparing with the slope-intercept form of the line equation
The slope of the line AB is m = 2
We know that the parallel lines have the same slope.
Thus, the slope of the new line is also 2.
now we have,
The slope of new line m = 2The point = (3, -2)Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 2 and the point (x₁, y₁) = (3, -2)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
y - (-2) = 2(x - 3)
y + 2 = 2x - 6
subtracting 2 from both sides
y + 2 - 2 = 2x - 6 - 2
y = 2x- 8
Therefore, the equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:
y = 2x- 8Select all of the equations that are not functions.
A) y=x^2
B) x² + y^2=3
C) y=4
D) x=3
Answer:
B
Step-by-step explanation:
x² + y² = 3 creates a circle and circles are not functions because one x-value relates to two y-values instead of one
Challenge , , and each went for a walk yesterday afternoon. walked
at a constant speed of
. walked
at a constant speed of
. walked for and at a constant speed of
. List the three people in order of the times they spent walking from least time to greatest time.
Which number label represents the nucleus? O 5 3 O 2
PLZ Answer needed ASAP
Answer:
option 1 I think i have had this before
Find the area of the following shape:
9514 1404 393
Answer:
77 in²
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = (1/2)bh
For your triangle, with its base of 14 inches and height of 11 inches, the area is ...
A (1/2)(14 in)(11 in) = 77 in²
_____
Additional comment
The side lengths added to the figure are incorrect. If we take the 11.5 to be correct, then the left side is about 15.3.
1/2×-7=1/3(×-12) solve
Answer:
X=18
Step-by-step explanation:
(1/2)*x-7 = (1/3)*(x-12) // - (1/3)*(x-12)
(1/2)*x-((1/3)*(x-12))-7 = 0
(-1/3)*(x-12)+(1/2)*x-7 = 0
x/2-1/3*(x-12)-7 = 0
(-1/3*2*(x-12))/2+x/2+(-7*2)/2 = 0
x-1/3*2*(x-12)-7*2 = 0
1/3*x-14+8 = 0
1/3*x-6 = 0
(1/3*x-6)/2 = 0
(1/3*x-6)/2 = 0 // * 2
1/3*x-6 = 0
1/3*x-6 = 0 // + 6
1/3*x = 6 // : 1/3
x = 6/1/3
x = 18
Cos 225°= what??????????
Which system of linear equations appears to have a solution of (3,0)?
Answer:
C
Step-by-step explanation:
-(-10)=?
Please help me with this equation!!
Answer:
+10
positive 10
:))))))))))
2/5 and 1/10 least common denominator
I need help please?!!!!
What is the slope, y-intercept and equation, marking Brainly .
Answer:
m=slope = 5
b=y intercept=-4
Step-by-step explanation:
Answer:
Slope=3/4, y-intercept=3.5, equation=y=3/4x+3.5
Step-by-step explanation:
Convert to militers
6 liters
OA 60,000 mililiters
OB. 6,000 mililiters
OC 600 milliliters
OD. 6 milliters
Answer:
B. because 6×1000 = 6000
evaluate for x = 3 and y =4 : (x^-2 y^2) / (x^0 y^3)
Answer:
1/36
Step-by-step explanation:
(3^-2 4^2) ÷ (3^0 4^3) = 1/36 (or in alternate form, 0.026 or 6^-2)
how to factor a quadratic
Answer:
To factor a quadratic polynomial use the equation
Step-by-step explanation:
F(x) = k{x2 - (sum of zeroes)x + (product of zeroes)}
The price of a new car was $22,800vin April. However, the price of the car was reduced 5% in May. Find the price in May.
Answer: 1140
Step-by-step explanation: Sorry if its wrong
Answer:21660
Step-by-step explanation:
95*22800/100