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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.

_____

<em>Estimating</em>

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.

_____

<em>Using the formula</em>

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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Our difference is 12. Our product is 81. What are the two numbers.

Delicious77 [7]

16.81665382639196787 x 4.81665382639196787

80.99999999999999982646270300946414412

All you have to do is figure out the rest of the decimal places. I couldn't go any farther. Good luck!

7 0

3 years ago

7) Simplify (5^10 x 7^14)^10 A. 5^20 x 7^24 B. 5^100 x 7^24 C. 5^100 x 7^140 D. 5^20 x 7^140

olga2289 [7]

(5^10 * 7^14)^10 =

5^(10 * 10) * 7^(14 * 10) =

5^100 * 7^140....its C....because ur multiplying the exponents

4 0

3 years ago

Read 2 more answers

HELP ME WRITE AN EQUATION FOR THIS GRAPH

kramer

Answer:

lol

Step-by-step explanation:

3 0

3 years ago

Two airplanes leave dallas at the same time and fly in opposite directions. One airplane travels 80 miles per hour faster then t

RSB [31]

recall d = rt, distance = rate * time.

let's say airplane A is going at a rate of "r", therefore airplane B is moving faster, at a rate of "r + 80".

now, after 3 hours, both planes have been travelling for 3 hours each, and say if A has covered "d" miles, then B has covered the slack of 2490 - d.

$\bf \leftarrow \underset{A}{\stackrel{r}{\rule[0.22em]{8em}{0.25pt}}}dallas\underset{B}{\stackrel{r+80}{\rule[0.22em]{18em}{0.25pt}}}\to \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ plane~A&d&r&3\\ plane~B&2490-d&r+80&3 \end{array}$

$\bf \begin{cases} \boxed{d}=3r\\ 2490-d=(r+80)(3) \end{cases} \\\\\\ 2490-\boxed{3r}=3r+240\implies 2250=6r\implies \cfrac{2250}{6}=r\implies \stackrel{A}{375}=r \\\\\\ \stackrel{B}{375+80\implies 455}$

4 0

3 years ago

Suppose a basketball player has made 223223 out of 406406 free throws. If the player makes the next 22 free throws, I will pay y

makkiz [27]

Answer:

Expected value E = $0.45

Step-by-step explanation:

Expected value E = P×w - P'×l

Where;

P = probability of making the next 2 throw.

P = 223/406 × 223/406 = 0.3017

P' = probability of not making a throw.

P' = 1 - P = 1 - 0.3017

P' = 0.6983

w = expected win = $20

l = Expected loss = $8

Substituting the values;

E = 0.3017 × $20 - 0.6983 × $8

E = $0.4476

Expected value E = $0.45

5 0

3 years ago