SOLUTION: How to derive Nth term of the following series? 1,3,6,10,15,21.........upto n terms 25!!!!!!!!!!!!!!!!!!!!!!!!!

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Question 166155: How to derive Nth term of the following series?
1,3,6,10,15,21.........upto n terms 25!!!!!!!!!!!!!!!!!!!!!!!!!
Found 2 solutions by 35qt, Fombitz:
Answer by 35qt(1) About Me  (Show Source):
You can put this solution on YOUR website!
25!!!!!!!!!!!!!!!!!!!!!!!!

Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the difference between terms,
1,3=2
3,6=3
6,10=4
10,15=5
15,21=6
.
.
.
First term=1
Second term=First term +2=1+2
Third term=Second term+3=1+2+3
Fourth term=Third term+4=1+2+3+4
Starting to see a pattern here...
Nth term=(N-1)term+N=1+2+3+...+(N-1)+N
Look like the terms follow,
T%5BN%5D=sum%28+i%2C+i=1%2C+N+%29
T%5B25%5D=sum%28+i%2C+i=1%2C+25+%29=325