Middle School

Q,2- A sequence is defined by the recurrence relation un+1 = 0.75u + 15, uo= 75, find the limit of this sequence​

Q 2 A sequence is defined by the recurrence relation un 1 0 75u 15 uo 75 find the limit of this sequence

Answer :

Answer:

60

Step-by-step explanation:

For a recurrence relation

[tex]u_{n+1}[/tex] = a[tex]u_{n}[/tex] + b

If - 1 < a < 1 then a limit exists and is calculated as

L = [tex]\frac{b}{1-a}[/tex]

Given

[tex]u_{n+1}[/tex] = 0.75[tex]u_{n}[/tex] + 15

with - 1 < 0.75 < 1

a = 0.75 and b = 15, thus

L = [tex]\frac{15}{1-0.75}[/tex] = [tex]\frac{15}{0.25}[/tex] = 60

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