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3 years ago

Find the next number in the series 3, 9, 81, 6561

Mathematics

2 answers:

nexus9112 [7]3 years ago

7 0

Answer:

19683

Step-by-step explanation:

you multiply each number times 3 so if you multiply the last number times 3 you should get your answer.

zhannawk [14.2K]3 years ago

7 0

Answer:

43046721

Step-by-step explanation:

the first number is 3

3*3=9

9*9=81

81*81=6561

therefore the next answer will be 6561*6561=43046721

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-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

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4 0

2 years ago

In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20

DiKsa [7]

The percentage of winning if 20 winning numbers are randomly selected from numbers 1 to 80 is 12.48%.

Given There are 80 numbers from which 20 numbers are selected randomly in a game of Keno by player and after selection of 20 winning numbers again 20 numbers are selected and player wins if the player has correctly selected 3,4,or 5 of the 20 winning numbers.

Probability is the chance of happening an event among all the events possible.

Probability of winning is calculated as under:

Probability= $C(20,3)C(60,17)/C(80,20)$

We have taken C(20,3) because player will win if 5 numbers are selected from 20 winning numbers.

We have taken C(60,17) because after selection of 20 numbers 60 numbers will left from 80 and after winning from 3 numbers 17 numbers left and from total 80, 20 numbers are taken.

=C(20,3)C(60,17)/C(80,20)

=(20!/3!17! * 60!/17!43!)/80!/20!60!

=1140*387221678682300/35353161422121743200

=12.48%

Hence the probability of winning is 12.48%.

Learn more about probability at brainly.com/question/24756209

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1 year ago