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2 years ago

What is the sum of the first five terms of a geometric series with a1 =20 and r =1/4?

1 answer:

5 0

The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,

Sn = (a1(1−r^n) / (1−r)

Substituting the known terms,
Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
Sn = 26.5625

Thus, the sum of the first four terms is 26.5625.

You might be interested in

78/17 round to the nearest 10

Alexus [3.1K]

Answer:

Step-by-step explanation:

78/17 gives 4.588

In rounding up numbers, 1 to 4 is rounded up to zero, while numbers 5 to 9 will be rounded up to 1.

In the question above, we are asked to round up to the nearest 10. And then 78/17 gives 4.588

This number is between 0 and 10.

The whole number there is 4. Therefore, 4 will be rounded up to Zero.

If the question and us to round up to the nearest whole number, as we have 4.588

The number before the whole number 4 is 5 (the tenth digit), and then 5 will be rounded up to 1. That 1 will hence be added to 4.

4+1= 5. To nearest whole number, it is 5 but to nearest ten, it is 0

7 0

3 years ago

How do i solve -18-6k=6(1+3k)

olga nikolaevna [1]

-1 is the answer to your question

5 0

3 years ago

A ball dropped from the top of a building can be modeled by the function f(t)=-16^2+36, where t represents time in seconds

Viefleur [7K]

Answer:

The ball is dropped from a height of 36 feet

The bee and the ball will collide after approximately 1.3 seconds

The bee and the ball will collide at approximately 8 feet above the ground

The ball hits the ground after 1.5 seconds

Step-by-step explanation:

The complete question is

A ball dropped from the top of the building can be modeled by the function f(t)=-16t^2 + 36 , where t represents time in seconds after the ball was dropped. A bee's flight can be modeled by the function, g(t)=3t+4, where t represents time in seconds after the bee starts the flight.

The graph represents the situation.

select all that apply

1) The bee launches into flight from the ground.

2) The ball is dropped from a height of 36 feet.

3) The bee and the ball will collide after approximately 1.3 seconds.

4) The bee and the ball will collide after approximately 8 seconds.

5) The bee and the ball will collide at approximately 8 feet above the ground.

6) The bee and the ball will not collide.

7) The ball hits the ground after 1.5 seconds

see the attached figure to better understand the problem

Verify all the options

case 1) The bee launches into flight from the ground.

The statement is false

Because

we have

$g(t)=3t+4$

For t=0

$g(t)=3(0)+4=4\ ft$

That means ----> The bee launches into flight from a height 4 feet above the ground

case 2) The ball is dropped from a height of 36 feet

The statement is true

Because

For t=0

$f(t)=-16(0)^2+36=36\ ft$

case 3) The bee and the ball will collide after approximately 1.3 seconds

The statement is true

Because

Equate f(t) and g(t)

$-16t^2+36=3t+4$

$-16t^2-3t+32=0$

solve the quadratic equation by graphing

The solution is t=1.324 sec

see the attached figure N 2

case 4) The bee and the ball will collide after approximately 8 seconds

The statement is false

Because, the bee and the ball will collide after approximately 1.3 seconds (see case 3)

case 5) The bee and the ball will collide at approximately 8 feet above the ground

The statement is true

Because

For t=1.324 sec

substitute the value of t in f(t) or g(t)

$g(t)=3(1.324)+4=7.97\ ft$

case 6) The bee and the ball will not collide

The statement is false

see case 3) and case 5)

case 7) The ball hits the ground after 1.5 seconds

The statement is true

Because

we know that

The ball hit the ground when the value of f(t) is equal to zero

For f(t)=0

$-16t^2+36=0$

$t^2=\frac{36}{16}$

$t=\frac{6}{4}=1.5\ sec$

4 0

2 years ago

Read 2 more answers

Estimate -9 1/6+2 1/3+(-1 7/8)

Eduardwww [97]

Answer:

-9

Step-by-step explanation:

-9+2-2=-9

5 0

2 years ago

Which ratios correctly compare bananas to apples, as shown in the picture ( 6 apples in a circle and 1 banana in the center ) ch

Licemer1 [7]

Answer:

6:1

Step-by-step explanation:

There are 6 apples t o1 banana

(This is all i can do would have been easier with picture)

5 0

2 years ago

Read 2 more answers