Question

Missing number in the series 9, ____, 6561, 43046721 is: 81 25 62 31 18 9. one number is 2 more than 3 times another. their sum is 22. find the numbers. 8, 14 5, 17 2, 20 4, 18 10, 12 10. the missing number in the series 1, 4, 27,____, 3125 is: 81 35 729 256 115 11. the next number in the series 3, 4, 6, 7, 9, 10 is: 12 11 15 17 13 12. a farmer is planting a straight row of crops with 3 feet between each plant. if 23 are planted, what is the distance between the first and last plant? 72 66 69 63 75

Answer 1

Alright, lets get started.

Missing number fom the series :  9, ..... , 6561, 43046721

43046721 is square of its previous number 6561, means

$6561^2 = 43046721$

It means the missing number will be square of its previous number

Means $9^2 = 81$, so missing number is 81.   :    Answer

Next : one number is 2 more than 3 times another. their sum is 22. find the numbers.

Suppose one number is x and second number is y

As per given equation, $x = 3y + 2$  ......equation (1)

Their sum is 22  means,  $x+y = 22$ .......equation (2)

Putting the value of x from equation1 into equation 2

$3y + 2 + y = 22$

$4y + 2 = 22$

Subtracting 2 in both sides

$4y + 2 - 2 = 22 - 2$

$4y = 20$

$y = 5$

$x = 22 - y = 22 - 5 = 17$

Means numbers are 17 and 5.   : Answer

Next : the missing number in the series 1, 4, 27,____, 3125 is

1 could be written as 1

4 could be written as $2^2$

27 could be written as $3^3$

So , next number would be $4^4$

$4^4 = 256$

Next one is $5^5 = 3125$

So, the missing number is 256   :    Answer

Next : the next number in the series 3, 4, 6, 7, 9, 10 is

After 3,4 (5) is mising, 6, 7 (8) is missing, 9, 10 (11) will be missing

So, next number will be 12.   : Answer

Next : a farmer is planting a straight row of crops with 3 feet between each plant. if 23 are planted, what is the distance between the first and last plant?

Between 2 plants, the distance is = $3 * (2-1) = 3$

Between 3 plants, the distance is = $3 * (3-1) = 6$

So, between 23 plants, the distance is = $3 * (23-1) = 3 * 22 = 66$

hene the distance between first and last plant woule be 66 feet.   :   Answer

Answer 2

The answers for each of the given question on series are;

A) 81

B) 5

C) 256

D) 12

E) 69

• A) We are given the series;

9, ____, 6561, 43046721

From this series, we can tell that;

First number is 9¹, third number is 81² and fourth number is 6561².

Thus,missing number is 81

• B) 2 more than 3 times another. their sum is 22.

Let the number be x. Thus;

3x + 2 + x = 22

4x = 22 - 2

4x = 20

x = 20/4

x = 5

• C) We have the series;

1, 4, 27,____, 3125.

First number is 1¹

Second number is 2²

Third number is 3³

Fifth number is 5^(5)

Thus;

Missing number is 4⁴ = 256

• D) We are given the series;

3, 4, 6, 7, 9, 10,...

Difference is alternating as;

+1, +2, +1, +2, +1, +2

Thus,next number is 10 + 2 = 12

• E) distance between each plant = 3 ft.

23 plants are planted. Thus;

Distance between first and last plant = 3 × 23 = 69 ft

Read more about arithmetic sequence at; https://brainly.com/question/7849474