Question 1210224
<br>
According to the definition of the sequence, each sequence is of the form<br>
n, n+1, 2n+2<br>
The numbers that can be used are the integers from 0 to 100, inclusive.  So the "last" sequence is the one in which 2n+2 is equal to 100.<br>
2n+2 = 100
2n = 98
n = 49<br>
The "first" sequence is clearly the one in which n is 0.<br>
So the sequences that satisfy the conditions of the problem are those where n is from 0 to 49, inclusive, which means 50 such sequences.<br>
ANSWER: 50<br>