Q2. The sum of the 3rd term to the 7th in a geometric series is 3267. Find the first term if the common ratio is 3. (3 marks)​

Answers

Answer 1

Answer:

142884, Answer,

Step-by-step explanation:

The first term of a GP is 7, the ratio is 3. What is the sum of the 7th and 10th term?

Solution: In the given GP, a = 7 and r = 3.

The sum of the 7th and the tenth terms

= T7 +T10 = ar^6 + ar^9 = ar^6[1+r^3]

= 7*3^6[1+3^3]

= 5103*28

= 142884, Answer,

please mark brainliest

Answer 2

The first term of geometric series is, a = 363/82

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Give that;

Sum of T₃ and T₇ of geometric series = 3267

And, common ratio(r) = 3

Hence, To find first term (a) we can use formula as;

Tₙ = arⁿ⁻¹

Now,  put the value on formula;

T₃ = a(3)³⁻¹

T₃ = (3)²a

And, T₇ = a(3)⁷⁻¹

T₇ = (3)⁶a

Since, T₃ + T₇ = 3267

Hence,

(3)²a + (3)⁶a = 3267

3²(a + 3⁴a) = 3267

(a + 3⁴a) =363

a + 81a = 363

82a = 363

a = 363/82

Thus, The first term of geometric series is, a = 363/82

Learn more about the geometric sequence visit:

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Related Questions

Square A is a dilation of Square B. What is the scale factor?

Answers

The scale factor is 4/5

What compass heading represents 20° north of east?​

Answers

Answer:

45°

Step-by-step explanation:

Northeast (NE), 45°, halfway between north and east, is the opposite of southwest. Southeast (SE), 135°, halfway between south and east, is the opposite of northwest. Southwest (SW), 225°, halfway between south and west, is the opposite of northeast.

For the function g(x)=5x2+4x−5, find g(−5)

Answers

Answer:

100

Step-by-step explanation:

g(x)=5x^2+4x−5

Let x = -5

g(x)=5 ( -5)^2+4(-5)−5

     = 5*25 - 20 -5

     =125 - 25

    = 100

What is cos 10° cos 8° − sin 10° sin 8° equal to?

Answers

Answer:

Step-by-step explanation:

cos 10° cos 8° − sin 10° sin 8° = cos(10° + 8°) = cos(18°)

If 1, x, 5 and 15 are in proportion, then the value of x is
a. 5
b. 4
c. 3​

Answers

Answer:

3

Step-by-step explanation:

Here, 1:x =5:15

Solving which the value of x is 3.

What’s greater 7.8 mL or 0.78 L

Answers

Answer:

7.8 mL

Step-by-step explanation:

Answer:

.78 L

Step-by-step explanation:

Well, simple conversions

a milliliter is .0001 of a liter and 1 liter is 1000 mL, so we can safely say that .78 L is 780 mL, dwarfing the given 7.8 mL

Write an exponential function in the form y=ab^x that goes through points (0,10) and (9, 5120).

Answers

The form [tex]y=ab^x[/tex] has two unknowns, namely [tex]a[/tex] and [tex]b[/tex], so you would need to have two points to find the equation (which you do). Once you have your two points, you can create a system of equations by plugging in the x and y coordinates like below:

[tex]\left \{ {{10=ab^0} \atop {5120=ab^9}} \right.[/tex]

One thing you may remember is that ANY number to the power of 0 equals 1. Knowing that, we can replace [tex]b^0[/tex] in the first equation with 1. Since 1 multiplied by any number is just that same number, that leaves [tex]a[/tex] alone in the first equation.

[tex]\left \{ {{10=a} \atop {5120=ab^9}} \right.[/tex]

The first equation now tells us that [tex]a[/tex] is 10, so we can plug 10 in for [tex]a[/tex] in the other equation.

[tex]5120=10b^9[/tex]

Now we can divide both sides by 10 to isolate [tex]b^9[/tex].

[tex]512=b^9[/tex]

To get [tex]b[/tex] alone, we have to take the 9th root of both sides.

[tex]\sqrt[9]{512} =\sqrt[9]{b^9}[/tex]

That gives us:

[tex]2=b[/tex]

We can now plug [tex]a[/tex] and [tex]b[/tex] into the form they gave us to get:

[tex]y=10*2^x[/tex]

FIRST TO ANSWER GETS MARKED BRAINLEST! please look at picture. The probability that a student guesses the correct answer to a four-choice multiple choice question is P(correct) = 0.25. How many correct answers should a student expect to guess on a test with 56 four-choice multiple choice questions?
A student should expect to guess_______correct answers.

Answers

Answer:

14 answers  

Step-by-step explanation:

since there is 1/4 of a chance to get a question right by guessing you need to see what 1/4 of 56 is, which is 14

Solve the equation P=KTV for the letter K.

Answers

Answer:

K = [tex]\frac{P}{TV}[/tex]

Step-by-step explanation:

P = KTV

Divide both sides by TV

(P/TV) = K

Identify the independent variable in the following hypothesis:

A person's opinion on immigration reform is influenced by their age.

Answers

“a persons opinion” is the independent variable because it doesn’t depend on others things for it to make sense

A researcher is 95% confident that the interval from 5.2 hours to 7.8 hours captures u = the true mean amount of time
it takes to fully charge a battery pack.
Is it plausible that the true mean number of hours to charge all battery packs of this type may be 5?
O No, this is not a plausible value for the population mean, because 5 is within the 95% confidence interval.
No, this is not a plausible value for the population mean, because 5 is not within the 95% confidence interval.
O Yes, this is a plausible value for the population mean, because 5 is within the 95% confidence interval.
Yes, this is a plausible value for the population mean, because the lower bound of the confidence interval, 5.2, is
greater than 5.

Answers

Answer: Choice B

No, this is not a plausible value for the population mean, because 5 is not within the 95% confidence interval.

====================================================

Explanation:

The greek letter mu is the population mean. It has the symbol [tex]\mu[/tex] which looks like the letter 'u' but with a tail at the front or left side.

The question is asking if mu = 5 is plausible if the researcher found the 95% confidence interval to be 5.2 < mu < 7.8

We see that 5 is not in that interval. It's a bit to the left of 5.2

Since mu = 5 is not in the interval, it's not a plausible value for the population mean.

Have we ruled it out with 100% confidence? No. Such a thing is not possible. There's always room for (slight) error. The researcher would need to do a census to be fully confident; however, such practices are very time consuming and expensive. This is the main reason why statistics is important to try to estimate the population with a sample.

The length of a rectangular parking lot is 32 meters and the width is 20 meters. The parking lot is surrounded by a sidewalk that is x meters wide. Find the expression that represents the area of the parking lot, including the sidewalk.

Answers

The expression is:
32 X 20 + x

Hope that will help :)

Which equation best represents the line graphed above? x = –1 x = 1 y = –1 y = x – 1

Answers

I think you forgot the graph. Please add it.

Answer:

I believe the answer is A: x = - 1

LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN= 4x + 3 and MP = 8x -9

X=

Answers

Solution:

We know that:

Given diagonals: LN and MPLN and MP must be equal because they are diagonals of LMNP.LN = 4x + 3MP = 8x - 9

Since LN and MP must be equation, equation formed: 4x + 3 = 8x - 9

Let's simplify the equation to find x.

Subtracting 4x both sides.

[tex]4x + 3 = 8x - 9[/tex]=> [tex]4x - 4x + 3 = 8x - 9 - 4x[/tex]=> [tex]3 = 4x - 9[/tex]

Add 9 both sides.

=> [tex]3 = 4x - 9[/tex]=> [tex]3 + 9 = 4x - 9 + 9[/tex]=> [tex]12 = 4x[/tex]

Divide 4 both sides.

=> [tex]12 = 4x[/tex]=> [tex]\frac{12}{4} = \frac{4x}{4}[/tex]=> [tex]x = 3[/tex]

Now, let's find the length of each diagonal.

[tex]LN = 4x + 3 = 4(3) + 3 = 12 + 3 = 15 \space\ units[/tex][tex]MP = 8x - 9 = 8(3) - 9 = 24 - 9 = 15 \space\ units[/tex]

Diagonals are equal

[tex]\\ \rm\Rrightarrow 4x+3=8x-9[/tex]

[tex]\\ \rm\Rrightarrow -4x=-12[/tex]

[tex]\\ \rm\Rrightarrow x=-12/-4[/tex]

[tex]\\ \rm\Rrightarrow x=3[/tex]

is a pentagon similar to a quadrilateral

Answers

Answer:

no

Step-by-step explanation:

quad- 4

pent- 5

they have a different number of sides

A triangle has two sides of lengths 4 and 15. What value could the length of
the third side be? Check all that apply.

Answers

sqrt(209) or sqrt(241), assuming it’s a right triangle. Are there answer choices?

the total of 3/4 and a number is no more than 2
3/4=a fraction

Answers

Just write any number less than 5/4

Answer:

Step-by-step explanation:

Let the number be x

[tex]\dfrac{3}{4}+x \leq 2\dfrac{3}{4}\\\\\\\dfrac{3}{4}+ x \leq \dfrac{11}{4}[/tex]

Subtract 3/4 from both sides

[tex]\dfrac{3}{4}-\dfrac{3}{4}+x\leq \dfrac{11}{4}-\dfrac{3}{4}\\\\\\x \leq \dfrac{11-3}{4}\\\\\\x \leq \dfrac{8}{4}\\\\\\x \leq 2[/tex]

Answer:  Any number less than or equal to 2

Evaluate the expression. Write your answer in scientific notation.
(1.9 x 10^9) - 6,300,000 × (5.6 x 10^2)

Please solve this expression as a scientific notation when you answer and remember.​

Answers

Answer:

- 1.628 x 10^9

Step-by-step explanation:

(1.9 x 10^9) - 6,300,000 × (5.6 x 10^2) =  - 1628000000

 - 1628000000 = - 1.628 x 10^9

6 6 small bricks have the same mass as 5 large bricks. The mass of one small brick is 2.5 kg. What is the mass of one large brick?​

Answers

Since 6 small bricks have the same mass as 5 large bricks and the mass of one small brick is 2.5 kg, the mass of one of the large bricks is 3 kg

What is mass?

Mass is the quantity of matter in a physical body.

6 small bricks have the same mass as 5 large bricks.

let

the total mass of the small or large bricks = x

Therefore,

6 × 2.5 = x

x = 15 kg

Therefore, the mass of each large bricks can be calculated as follows:

let the mass of each large bricks  = y

15 = 5y

divide both sides by 6

y = 15 / 5

y = 3 kg

Therefore, the mass of one of the large bricks is 3 kg

.learn more on mass here: https://brainly.com/question/895643

Plss help mee
you need to show your work

At the school's fall bake sale, all of the pies were cut into 6 pieces, so each person who bought a piece bought 1/6 of a pie. Each slice of pie sold for $1.00. How much money did the school make if all eleven pies were sold? (In other words, find 11 divided by 1/6 .)​

Answers

Answer:

2 ⅓  

Step-by-step explanation:

division is the same as a fraction

the dividend is the numerator and the divisor is the denominator

7÷3 is the same as 7/3

change 7/3 into a mixed number which is 2 ⅓  

∠A and ∠B are complementary. The measure of ∠A is 21°.

What is the measure of ∠B?

Enter your answer in the box.
point theif = ban

Answers

Answer:

69°

Step-by-step explanation:

Complementary angles sum to 90°.

We have the measure of one angle, find the missing one as below.

m∠A + m∠B = 90°21° + m∠B = 90°m∠B = 90° - 21°m∠B = 69°
<B be x

Complementary angles have sum 90°

[tex]\\ \sf\longmapsto x+21=90[/tex]

[tex]\\ \sf\longmapsto x=90-21[/tex]

[tex]\\ \sf\longmapsto x=69[/tex]

Brandon is half of Ella's age. Ella is three times Tristans age. In fifteen years, their combined age will be 89. How old is Brandon?

Answers

Answer:

Step-by-step explanation:

Let Brandon's age be [tex]x[/tex]

Therefore Ella=[tex]2x[/tex]

Tristan= [tex]\frac{2x}{3}[/tex]

Fifteen years time add 15 to each age

Brandon: [tex]x+15[/tex]

Ella: [tex]2x+15[/tex]

Tristan:[tex]\frac{2x}{3} +15[/tex]

All their ages together=89

So: [tex]x+15[/tex] +  [tex]2x+15[/tex] + [tex]\frac{2x}{3} +15[/tex][tex]=89[/tex]

[tex]3\frac{2}{3} x=44[/tex]

[tex]x= \frac{44}{3\frac{2}{3} } =12[/tex]

3 x
Abigail keeps track of the number of pages she reads. Last year, she read 5,473 pages. The year before,
she read 2,379 pages. Select all of the choices that are good estimates by rounding to place values for the
total pages Abigail read over the two years.
A. 7,000
B. 7,500
C. 7.850
D. 7.900
E. 8,000

Answers

Answer:

A, C, and E I think

Step-by-step explanation:

Real answer=5473+2379=7852
Possible answers/estimates would be:
C
D
E

What is -86 + x = - 4x + 29

Answers

Answer:

x = 23

Step-by-step explanation:

Add 4x to the left and add 86 to the right.

5x = 115

Now, divide 5 on both sides to get x.

x = 23.

The result is 23.

Answer:

x= – 115/3

Step-by-step explanation:

I don’t know what exact form you want so I’ll give you mixed number form.

a box of 40 chocolates contains 56g of saturated fat. How much saturated fat is there in 1 chocolate

Answers

Divide total fat by number of chocolates


56/40 = 1.4 grams


answer: 1.4 grams

F(x)=2x^2-5x g(x)=-3x^2 find f(2)

Answers

F(x)= 2(2)^2-5(2)= -2 that’s it

Convert 63° to radians.

Answers

Answer:

1.1025rad

Step-by-step explanation:

1°=0.0175rad

63°=0.0175rad*63=1.1025rad

help what are angles 3, 6, 8, 9, 11, 13, 14, 15, 16, 17, and 18

Answers

3. 128°

6. 136°

8. 96°

9. 96°

11. 136°

13. 52°

14. 128°

15. 44°

16. 136°

17. 128°

18. 52°

write an equation of the line below​

Answers

Answer:

y=3x

Step-by-step explanation:

which of the following is a graph of a line with the equation 3y-4x=-3​

Answers

The answer would be the second choice. Hope this helps and please mark brainliest!
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