Prove that the sequence is monotonically decreasing

Give the sequence:$a_1 = 1, a_{n+1}=72/(1+a_n)$

In Thomas' Calculus: Early Transcendentals, exercise 10.1 question 91, they asked to assume that the above sequence converges and to evaluate the limit.

But I am unable to prove monotonicity using induction.

I tried using induction as follows:Let $a_{k+1}< a_k$

$1+a_{k+1}< 1+a_k$

$72/(1+a_{k+1})> 72/(1+a_k)$

$a_{k+2}> a_{k+1}$ ----- not decreasing

Where am I going wrong?

I evaluated the values as:$a1=1, a_2=24, a_3=2.88, a_4=18.55, a_5=3.68$. Clearly it's not monotonic. So am I just supposed to assume monotonicity?