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Mariulka [41]
3 years ago
14

Jake has a bag of 50 beads, of which some are red and the remaining are yellow. Jake randomly pulls out a bead from the bag, rec

ords the color, and replaces it in the bag. Jake has already recorded 9 red and 6 yellow beads. Based on the result, what is most likely the number of red beads in the bag?
A. 10
B. 20
C. 30
D. 60
Mathematics
1 answer:
s2008m [1.1K]3 years ago
3 0
The answer is c dont know if im right sorry
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Check the forward differences of the sequence.

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b_{n+1} = b_n + 2

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and so on down to

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We solve for a_n in the same way.

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

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

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