A sequence {an}∞n=0 is defined by the following formula. What is the limit of this sequence?a0 = 1, an = 13 (an−1 + 3), for n ≥ 1

To find the limit of the sequence, we need to first understand the pattern of the sequence.

Given the formula an = 13(an−1 + 3), we can see that each term is 13 times the previous term plus 39.

Let's calculate the first few terms of the sequence:

a0 = 1 (given)

a1 = 13(a0 + 3) = 13(1 + 3) = 52

a2 = 13(a1 + 3) = 13(52 + 3) = 715

a3 = 13(a2 + 3) = 13(715 + 3) = 9334

From these calculations, we can see that the sequence is increasing rapidly.

In general, if a sequence {an} has the property that an = k(an−1 + c) for some constants k and c, and if k > 1, then the sequence will increase without bound as n increases.

Therefore, the limit of the sequence {an} as n approaches infinity is infinity.