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# 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.

Thanks

### 1 Answer

- BenLv 710 years agoFavorite Answer
a)

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

b)

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