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Vadim26 [7]
2 years ago
15

​ c(1)=−20 c(n)=c(n−1)+10 ​ Find the 2nd term in the sequence.

Mathematics
1 answer:
Bad White [126]2 years ago
3 0

Answer:

-10 is the second term.

Step-by-step explanation:

After the first term each term is obtained from the previous one by adding 10.

c(1) = -20

so c(2) = -20 + 10

= -10.

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Step-by-step explanation:

First take into account the concept of combination and permutation:

In the permutation the order is important and it is signed as follows:

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In the combination the order is NOT important and is signed as follows:

C (n, r) = n! / r! (n - r)!

Now, to start with part a, which corresponds to a combination because the order here is not important. Thus

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C (10, 2) = 10! / 2! * (10-2)! = 10! / (2! * 8!) = 45

There are 45 possible scenarios.

Part b, would also be a combination, defined as follows

n = 10

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Therefore, several cases must be made:

C (10, 0) = 10! / 0! * (10-0)! = 10! / (0! * 10!) = 1

C (10, 1) = 10! / 1! * (10-1)! = 10! / (1! * 9!) = 10

C (10, 2) = 10! / 2! * (10-2)! = 10! / (2! * 8!) = 45

C (10, 3) = 10! / 3! * (10-3)! = 10! / (2! * 7!) = 120

The sum of all these scenarios would give us the number of possible total scenarios:

1 + 10 + 45 + 120 = 176 possible total scenarios.

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252 possible scenarios to be the same amount of heads and tails.

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