Well I'm a 15 year old teen.im really into serious relationships and I have been going out with my girlfriend for about a month and a half now.I am really in love with her.. and she says she's in love with me, but sometimes she just doesn't seem happy to see me or when we are texting she isn't talkative all that much about half the time (latley) we get into arguments once in awhile.and I just really don't know what to think.ive had a lot of things like this in the past and I don't want it to end up the same way with her.I am her first serious boyfriend.

Sorry guy, there is no such thing as a serious relationship after a month and a half, especially not at 15.

That's where most people screw things up, because they don't understand the partner they have, and forget the "have fun getting to know each other " phase that is so important when we get together with some one.

I think if you relax, and have fun together,as you get to know each other as partners, you will see that its your insecurities, and expectations that are off here, not your partner, as a relationship is a blend between two people, not a set of rules to be followed strictly by one persons idea of how things work.

If you want different results from your other experiences, you have to change your thinking, NOT hers.

Have some fun getting to know your partner, and let her learn YOU!

At the age of 15 it's what they say "Puppy love". When you get older you will experience more about love. So don't focus on this matter..

Well first off, your 15 bro don't worry you have your whole life ahead of you to find someone.. your whole life. Think about it.
Secondly, well the fact that you said you're her first serious boyfriend gives it away. She's new to all of this she doesn't know how to react with certain situations you know. She's not all that expierienced with all the seriousness(if that's even a word). I say talk to her. Tell her how you feel. Start with you love her and you don't want to loose her (girls LOVE all that crap) then ask her how she feels with the whole relationship.
I wish you good luck :D