The sequence an is defined by the recurrence relation an1 0

The sequence {a_n} is defined by the recurrence relation a_n+1 = 0.4an + 6 with a_0 = 4 Find a_1 = a_2 = a_3 = Find Algebraically what value does this sequence converge to?

Solution

given that the sequence converges and it converges to 10.

Given that a₀=4,and the codition that a_n+1= 0.4a_n+6

if we substitute n=1,2,3,4,5,.....we will get the values of a₁,a₂,a₃,a₄.....as 4 ,7.6   ,9.616,    9.8464,   9.93856........

As we proceed like this the sequence converges to a limit 10.

hence the value for the sequence at which it converge is 10.