Find the first four terms of each of the recursively defined sequences in 1–-8. 1. az = 2ax-1 +k, for all integers k > 2 %3D aj = 1 2. b = bị-1 + 3k, for all integers k > 2 bi = 1 %3D 3. c = k(ck-1)², for all integers k > 1 co = 1 4. dį = k(dz-1)², for all integers k > 1 do = 3 %3D 5. St = Sk-1 + 2sk-2, for all integers k > 2 So = 1, s = 1 6. t = tk-1 + 21k-2, for all integers k > 2 to = -1, t = 2 7. uz = kuz-1 – Uz-2, for all integers k > 3 uj = 1, u2 = 1 %3D 8. Vk = Vk-1 + Vk-2 + 1, for all integers k > 3 Vi = 1, vz = 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#2, #4, #8

Find the first four terms of each of the recursively defined
sequences in 1–-8.
1. az =
2ax-1 +k, for all integers k > 2
%3D
aj = 1
2. b = bị-1 + 3k, for all integers k > 2
bi = 1
%3D
3. c = k(ck-1)², for all integers k > 1
co = 1
4. dį = k(dz-1)², for all integers k > 1
do = 3
%3D
5. St = Sk-1 + 2sk-2, for all integers k > 2
So = 1, s = 1
6. t = tk-1 + 21k-2, for all integers k > 2
to = -1, t = 2
7. uz = kuz-1 – Uz-2, for all integers k > 3
uj = 1, u2 = 1
%3D
8. Vk = Vk-1 + Vk-2 + 1, for all integers k > 3
Vi = 1, vz = 3
Transcribed Image Text:Find the first four terms of each of the recursively defined sequences in 1–-8. 1. az = 2ax-1 +k, for all integers k > 2 %3D aj = 1 2. b = bị-1 + 3k, for all integers k > 2 bi = 1 %3D 3. c = k(ck-1)², for all integers k > 1 co = 1 4. dį = k(dz-1)², for all integers k > 1 do = 3 %3D 5. St = Sk-1 + 2sk-2, for all integers k > 2 So = 1, s = 1 6. t = tk-1 + 21k-2, for all integers k > 2 to = -1, t = 2 7. uz = kuz-1 – Uz-2, for all integers k > 3 uj = 1, u2 = 1 %3D 8. Vk = Vk-1 + Vk-2 + 1, for all integers k > 3 Vi = 1, vz = 3
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