Find numbers $a_n$ such that $a_n > a_{n+1}$ and $a_n, a_{n+1}$ that satisfies the inequality $a_n geq frac{1}{(n+1)^2} + a_{n+1}$

I’m working on a project for my introduction to abstract math course and I’m stuck on a particular part of it. We’re supposed to prove $sum_{k=1}^{n} frac{1}{k^2} < frac{7}{4}$ using induction, and the project has us use the stronger inequality of $sum_{k=1}^{n} frac{1}{k^2} leq frac{7}{4} – a_n$, with $a_1, a_2, : cdots :, a_n,: cdots $ being positive numbers such that the inequality is true for all $n in mathbb{Z}^+$. I found an inequality that I could use to come up with something for $a_n$, which is $a_n geq frac{1}{(n+1)^2} + a_{n+1}$. Here’s where I got stuck, as I don’t know what would be a good sequence to define $a_n$ as that would make proving $sum_{k=1}^{n+1} frac{1}{k^2} leq frac{7}{4} – a_{n+1}$ the easiest, or even what sequence to use at all.