Question 752003: For questions 3-5, find the first 4 terms and the 8th term of the recursively-defined sequence.
3. b1 = 2 and bk+1 = 3bk, for k>0
4. v1 = 0.75 and vn = (-2)vk-1 for n>1
5. c1 = 2, c2 = -1, and ck+2 = ck + ck+1 for k>0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the first 4 terms and the 8th term of the recursively-defined sequence.
3. b1 = 2 and bk+1 = 3bk, for k>0
b(1) = 2
b(2) = 3*b1 = 3*2 = 6
b(3) = 3*b2 = 3*6 = 3^2*2 = 9*2 = 18
b(4) = 3*b3 = 3*3^2*2 = 3^3*2 = 54
----
b(8) = 3^4*2 = 81*2 = 162
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4. v1 = 0.75 and vn = (-2)vk-1 for n>1
v(1) = 3/4
v(2) = -2(3/4)
v(3) = (-2)^2(3/4) = 3
v(4) = (-2)^3(3/4) = -6
----
v(8) = (-2)^6(3/4) = 48
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5. c1 = 2, c2 = -1, and ck+2 = ck + ck+1 for k>0
c(1) = 2
c(2) = -1
c(3) = 2+-1 = 1
c(4) = -1 + 1 = 0
----
c(8) = c(6) + c(5) = [c(4)+c(5)] + c(5) = [0+1+1] = 2
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Cheers,
Stan H.
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