Q:

Position of 提供 in 这椅子是专为老年人提供的

这椅子是专为老年人提供的. This chair is provided for the old man. 

I don't understand why 提供 is at the end of sentence. I thought 提供 could be placed before 专为. 

A:

It is all because of that 为
Basically the following two sentences have the same meaning:
这椅子是专门提供给老人的
这椅子是专(门)为老人提供的
English translation will be:
We provided this chair specifically for the elders
It is actually quite common to use the 为 to move the verb after the subject to emphasize the "for" 
For example,
My heart only beats for you
我的心只为你跳动

