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2 years ago

What is the next term in the number pattern? 21, 31, 36, 46, 51, … Enter your answer in the box.

Mathematics

2 answers:

Evgen [1.6K]2 years ago

8 0

Answer:

Step-by-step explanation:

Leni [432]2 years ago

7 0

Answer:

Step-by-step explanation:

first it goes up by 10 then 5 now 10

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Is pi is more accurate than an answer that uses 3.14 for pi ?<br> .

Burka [1]

Answer: yes because pi = 22/7 as a fraction and as a decimal that never terminates

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6 0

3 years ago

Which expression is equivalent to (r^-7)^8

ahrayia [7]

Answer:

1/r^56

Step-by-step explanation:

Not sure if you did a typo there or what cus 7 x 8 should be 56

Whenever the power of a number is negative, you flip. So r^-7 becomes 1/r^7

Remove the bracket and distribute 8 to the power of 1 and r^7

1 to the power of 8 will still be 1, r^7 x 8 = r ^ 56

6 0

2 years ago

Someeee one?????????????????

Ad libitum [116K]

Answer:

Option B) $a_{n} = 2\cdot 4^{n-1}$

Step-by-step explanation:

The given geometric sequence is

2, 8, 32, 128,....

The general form of a geometric sequence is given by

$a_{n} = a_{1}\cdot r^{n-1}$

Where n is the nth term that we want to find out.

a₁ is the first term in the geometric sequence that is 2

r is the common ratio and can found by simply dividing any two consecutive numbers in the sequence,

$r=\frac{8}{2} = 4$

You can try other consecutive numbers too, you will get the same common ratio

$r=\frac{32}{8} = 4$

$r=\frac{128}{32} = 4$

So the common ratio is 4 in this case.

Substitute the value of a₁ and r into the above general equation

$a_{n} = 2\cdot 4^{n-1}$

This is the general form of the given geometric sequence.

Therefore, the correct option is B

Note: Don't multiply the first term and common ratio otherwise you wont get correct results.

Verification:

$a_{n} = 2\cdot 4^{n-1}$

Lets find out the 2nd term

Substitute n = 2

$a_{2} = 2\cdot 4^{2-1} = 2\cdot 4^{1} = 2\cdot 4 = 8$

Lets find out the 3rd term

Substitute n = 3

$a_{3} = 2\cdot 4^{3-1} = 2\cdot 4^{2} = 2\cdot 16 = 32$

Lets find out the 4th term

Substitute n = 4

$a_{4} = 2\cdot 4^{4-1} = 2\cdot 4^{3} = 2\cdot 64 = 128$

Lets find out the 5th term

Substitute n = 5

$a_{5} = 2\cdot 4^{5-1} = 2\cdot 4^{4} = 2\cdot 256 = 512$

Hence, we are getting correct results!

6 0

3 years ago

Shannon Perfumeries sells two fragrances. The table contains the price corresponding to the number of bottles of fragrance A. Bo

Aliun [14]

<span>Table
Bottles Price($)
3           78
6           156
9           234

From that you can find the unit price: 78 / 3 = 156 / 6 = 234 / 9 = 26.

That means that the unit rate of this fragance is $26.

If you call x the number of bottles the equation is

Price = unit rate * number of bottles = 26x.

Now compare this information with that on your graph to compare the unit rates.

This can help you fo find the unit rate in from your grpah: the unit rate is the slope of the line =

[change in y-coordinate] / [change in the x-coordinate]
</span>

5 0

3 years ago

Read 2 more answers

A firm manufactured 1000 Tv sets during its first yeae the total firns production during 10 years of operation is 29035 sets If

Alexus [3.1K]

Answer: the increase each year is 423 tv sets

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 10 years

a = 1000

S10 = 29035

We want to determine d which is the amount by which the production increased each year. Therefore, the sum of the first 10 years would be

29035 = 10/2[2 × 1000 + (10 - 1)d]

29035 = 5[2000 + 9d]

29035/5 = [2000 + 9d]

9d = 5807 - 2000 = 3807

d = 3807/9 = 423

3 0

3 years ago