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3 years ago

What is the sum of the geometric sequence 3,12,48... if there are 8 terms?

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

6 0

Answer:

C) 65,535

Step-by-step explanation:

You can add up the 8 terms ...

3, 12, 48, 192, 768, 3072, 12288, 49152

to find their sum is 65535.

_____

Estimating

Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.

_____

Using the formula

You know the formula for the sum of a geometric sequence is ...

S = a1(r^n -1)/(r -1)

where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).

Filling in the values, you find the sum is ...

S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535

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A mathematics journal has accepted 14 articles for publication. However, due to budgetary restraints only 7 articles can be publ

butalik [34]

The total number of articles is 14 and only 7 can be published. Since what is asked is the ways to assemble the 7 articles, this is a permutation problem.
14P7 = 17297280 ways
If order is not of concern, the problem is just a combination problem
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7 0

4 years ago

Read 2 more answers

You invest $5000 in an account at 5.5% per year simple interest. How much will you have in the account at the beginning of the 6

NeX [460]

Answer:

The amount in the account in the beginning of the 6th year is $6375 .

Step-by-step explanation:

Formula

$Simple\ interest = \frac{Principle\times Rate\ times Time}{100}$

As given

You invest $5000 in an account at 5.5% per year simple interest.

Principle = $ 5000

Rate = 5.5 %

Time = 5 years

(As calculate amount in the account for beginning of 6th year.)

Putting all the values in the formula

$Simple\ interest = \frac{5000\times 5.5\times 5}{100}$

$Simple\ interest = 50\times 5.5\times 5$

Simple interest = $ 1375

Amount = Principle + Simple interest

Putting values in the above formula

Amount = $5000 + $1375

Amount = $ 6375

Therefore the amount in the account in the beginning of the 6th year is $ 6375 .

8 0

3 years ago

Solve -3(-2x+20)=-8(x+12)+92 please?

sveta [45]

The answer is x=4 hope it helps

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3 years ago

A standard deck of playing cards has 52 cards total that contains 13 of each suit (hearts, diamonds, clubs and spades). What is

schepotkina [342]

Answer:

C 1/2

Step-by-step explanation:

There are 4 suits, 2 suits are red (hearts and diamonds) while 2 are black (clubs and spades)

Since 13 cards are in each suit, 26 cards are red ( 2 * 13)

There are 52 total cards

P (red) = red cards/ total cards

= 26 / 52

= 1/2

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3 years ago

Can y’all help me on question 14?!

ExtremeBDS [4]

Answer:

The answer is 3.2

Step-by-step explanation:

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3 years ago