Why is the narrator motivated to travel to India?

It seems that the narrator is intrigued by Olivia's mysterious letters. The fact that they were kept hidden for so long, and that neither Tessie nor Beth will speak of Olivia, seems to incite her curiosity. The narrator hardly remembers Douglas, but does recall Tessie quite well. It's likely that she sees this as both a mystery to unravel and an adventure at this point in her young life.