A sequence is recursively defined by a (n) = a (n - 1) + 2 a (n - 2), for n > 2. If a (1) = 0 and a (2) = 1, what is the value of a (6)?
(A) 5
(B) 8
(C) 11
(D) 13
(E) 21
recursively defined
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- sanju09
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a(6) = a(5) + 2a(4)
a(3) = a(2) + 2a(1) implies a(3) = 1
a(4) = a(3) + 2a(2) implies a(4) = 1 + 2 = 3
a(5) = a(4) + 2a(3) implies a(5) = 3 + 2 = 5
So, a(6) = 5 + 2(3) = 11
The correct answer is (C).
a(3) = a(2) + 2a(1) implies a(3) = 1
a(4) = a(3) + 2a(2) implies a(4) = 1 + 2 = 3
a(5) = a(4) + 2a(3) implies a(5) = 3 + 2 = 5
So, a(6) = 5 + 2(3) = 11
The correct answer is (C).
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- kmittal82
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Hmm, there is probably a quicker way of doing this, but here goes:
a(6) = a(5) + 2a(4)
Now,
a(5) = a(4) + 2a(3) - eq 1
a(4) = a(3) + 2a(2) - eq 2
a(3) = a(2) + 2a(1) => a(3) = 1
Putting in eq 2
a(4) = 1 + 2(1) = 3
Putting this in eq 1
a(5) = 3 + 2(1) = 5
Finally, a(6) now becomes => 5 + 2(3) = 11
So, the answer should be (C)
a(6) = a(5) + 2a(4)
Now,
a(5) = a(4) + 2a(3) - eq 1
a(4) = a(3) + 2a(2) - eq 2
a(3) = a(2) + 2a(1) => a(3) = 1
Putting in eq 2
a(4) = 1 + 2(1) = 3
Putting this in eq 1
a(5) = 3 + 2(1) = 5
Finally, a(6) now becomes => 5 + 2(3) = 11
So, the answer should be (C)