more Recurrence relations?
can someone help me with this please ?
A sequence satisfies the relation Vn+1 = PVn + 4, Vo=3
a) Express V1 and V2 in terms of P.
b) Given that V2 = 8, find the value of P that produces a sequence with no limit.
- BenLv 710 years agoFavorite Answer
Use the relation to compute each value:
V1 = PVo + 4 = 3P + 4
V2 = PV1 + 4... plug in V1
= P(3P + 4) + 4
= 3P^2 + 4P + 4
Set V2 equal to 8, and solve for P:
V2 = 3P^2 + 4P + 4 = 8... now solve the quadratic
3P^2 + 4P - 4 = 0... factor
(3P - 2)(P + 2) = 0... solve
P = 2/3; P = -2
Of these two values, P=-2 is the one that produces a sequence with no limit