SOLUTION: Let b0, b1, b2, be the sequence defined by the explicit formula bn = C · 5^n + D(−4)^n for each integer n ≥ 0, where C and D are real numbers. (a) Find C and D so that

Question 1167598: Let
b0, b1, b2, be the sequence defined by the explicit formula
bn = C · 5^n + D(−4)^n for each integer n ≥ 0,
where C and D are real numbers.
(a)
Find C and D so that
b0 = 0
and
b1 = −9.
b) Find C and D so that
b0 = 4
and
b1 = 11.
c)What is
b2 in this case?
Answer by Resolver123(6) (Show Source): You can put this solution on YOUR website!
(a) for
means that , by hypothesis, after direct substitution.
Also, inserting into the formula gives .
Hence, .
From c + d = 0, we get d = -c.
Substituting this into the equation 5c - 4d = -9 gives 5c - 4(-c) = 5c+4c = -9,
or 9c = -9, or c = -1.
Therefore, c = -1, and d = -(-1) = 1.
(b) Similarly, gives , or c + d = 4, or d = 4 - c. Also, , or 5c - 4d = 11.
Substituting, 5c - 4(4 - c) = 11, or 5c - 16 + 4c = 11.
This gives 9c = 27, or c = 3, which consequently gives d = 4 - 3 = 1.
(c) From part (b), we get , so that

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