A sequence u1, u2, u3, … is defined by

u1=4 and un+1= 2/un for n≥1
a. Write down the values of u2 and u3
b. Describe the behaviour of the sequence

please help me

un1 = 4

un2 = 4=2/4 = 1/2
un3 = 2/(1/2) = 4
un4 = 2/4 = 1/2
un5 = 2/ (1/2) = 4
un6 = 2 /4 = 1/2
well there is a certain predictability to this :)

How to calculate

u2

To find the values of u2 and u3, we can use the given recursive relation:

u1 = 4
un+1 = 2/un

a. Finding the value of u2:
Using the recursive relation, we can substitute n = 1:

u2 = 2/u1
u2 = 2/4
u2 = 1/2

Therefore, the value of u2 is 1/2.

b. Finding the value of u3:
Again, using the recursive relation and substituting n = 2:

u3 = 2/u2
u3 = 2/(1/2)
u3 = 2 * 2/1
u3 = 4

Therefore, the value of u3 is 4.

Now, let's describe the behavior of the sequence:

The given sequence is defined recursively, where each term (n+1) is calculated by dividing 2 by the previous term (n) throughout the sequence.

In this case, we can observe that as n increases, the terms oscillate between decreasing and increasing values. Initially, the sequence starts with a high value of 4 (u1 = 4), then it decreases to 1/2 (u2 = 1/2), and finally increases to 4 again (u3 = 4).

Since each term is calculated by taking the reciprocal of the previous term and multiplying by 2, the sequence will continue to alternate between decreasing and increasing values as we proceed.

Therefore, we can conclude that the behavior of the sequence is oscillatory, with the terms alternating between decreasing and increasing values.