37. Consider the sequence v30, \\ 30 + v30, \\/ 30 + \\ 30 + V30, ... (a) Define the sequence recursively. (b) Assuming the sequence converges to some limit L, find L. 38. Consider the sequence {an} - that has the following recursive definition: an+1 = 10 - an for integers n 2 1. (a) Assuming the sequence converges to some limit L, find L. (b) How must a, be defined to ensure that the sequence converges? Justify your answer. 39. The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, ... begins with two l's and thereafter each term in the sequence is the the sum of previous two terms. (a) Define the Fibonacci sequence recursively.(b) Clearly the Fibonacci sequence diverges to too, but consider the ratio of succes- sive terms an+1 for n > 1, i.e an 1 23 5 8 1'1' 2' 3'5' Assuming this "ratio sequence" converges to some limit L, find L