Identify fruit tree

A fruit tree sprouted in our back yard. We thought it was an avocado tree by the leaves and the small roundish dark green fruit that came out. Eventually the fruit has turned from nubby to softer flesh, lighter green and then yellow. If you cut one open, it has small seed clusters the size and color of sesame seeds and it's pinkish inside. Smells like a grapefruit almost. Does anyone have any ideas what it is? The leaves are about 5-6 inches long, single not clusters..look almost identical to avocado leaves.

 

Looks like guava.

 

Thanks very much...I've read some on it, but does anyone have any great recipes for it?

 

It looks like a guava and it is a guava.
I love the smell and aroma of a guava fruit. Just an hour ago I was in a grocery store. They had advertised guava for $1.50 a piece. I wanted a couple but only one, the last one, was left and it was not in good shape. Not all guava species may have the enchanting smell and aroma but the one that do are just irresistible.
I bought a plant last spring that I am growing in a 5 gallon pot in Zone 5. Believe me it grew fast during the summer and had white jasmine like flowers and then fruits. Alas, one night in September the raccune got to it first and got every piece of fruit off the tree and breaking the tree leader branch by climbing. Not a trace of the fruit was left even though the fruits were not ripe yet! The plant is now inside for overwintering, but it has been more than a month and I am still thinking of that raccune and imagining a sharp pointed fork in my hands (because i had been warned of raccune strength when it is provoked).
So you take care of that tree in your backyard. It will reward you.

 

racoons are little devils, I just cleaned up the garbage they helped themselves to from our garbage bin outside.

 

Four years ago I ate a guava and put the seeds in my hot pepper pot, three months later lots of guava plants came up. Non of my friend wanted so I only save one in my house and one in my husband office. Six months later, the one in my house grow slowly, but the other one was 3,4 ft tall and flowers and 18 baby guavas. By the end of Nov that year only 10 of the guavas left when it inside my house and sadly only 3 are matured and riped. Can anyone help please, my Meiwa kumquat, Key lime, Meyer lemon does the samething. Thanks, et2007.