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3 years ago

Compare the quantity in column A with the quantity in column B. Choose the best answer.

Mathematics

1 answer:

love history [14]3 years ago

6 0

Answer:

C. The two quantities are equal

Step-by-step explanation:

Column A

Substitute the numbers with the letters

an = a1 + (n - 1) d should be an = 2 + (8 - 1) 5

Work it out, you should get 37

Column B

Substitute the numbers with the letters again

an = a1 + (n - 1) d should be an = 13 + (9 - 1) 3

Work it out, your answer should be 37 as well

Tada, done. The answer is C.

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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

Simon is creating a flower arrangement. A client asked him to select 4 of the 7 available flower options to create the arrangeme

SashulF [63]

Answer:

i dont know but good luck! <3

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The sequence a, = 2, 4, 8, 16, 32, ... is the same as the sequence ay = 2,

blondinia [14]

Answer:

TRUE

Step-by-step explanation:

TRUE

a_1 = 2

a_n = 2*(an_1)

if we start with 2, we would get

a_2 = 2*(a_1) = 2*(2) = 4

a_3 = 2*(a_2) = 2*(4) = 8

a_4 = 2*(a_3) = 2*(8) = 16

a_5 = 2*(a_4) = 2*(16) = 32

and so on

4 0

3 years ago

Find the surface area of a triangular prism that has the following dimensions. Use the formula SA = 2B + Ph.

OverLord2011 [107]

Answer: The surface area of the triangular prism is 448 square millimeters.

To find the surface area, we just need to input our values into the formula that is given.

SA = 2B + Ph
SA = 2(84) + 56(5)
SA = 168 + 280
SA = 448

The final surface area is 448 mm^2.

7 0

3 years ago

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Solve the inequality 3x - 5 < 4.

Pachacha [2.7K]

Answer:

x < 3

Step-by-step explanation:

Since 3x - 5 < 4 then we can transpose the inequality to make x the subject of the equation:

If 3x - 5 < 4

⇒ 3x < 4 + 5

⇒ x < 9 ÷ 3

⇒ x < 3

8 0

3 years ago