Question 169809: my teacher gave me a homework about sequences.He told us to find the rule between
1,3,6,10,15,21,can you show the working please and i have to sumit it today.ISBN ACTIVE MATHEMATICS 2 PG 44 EXERCISE 6
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! There are many ways to find the sequence, but here's a little trick
1,3,6,10,15,21 ... Start with the given sequence
2,6,12,20,30,42 ... Multiply EVERY term by 2
So we now have the sequence
2,6,12,20,30,42
So if we start at n=1, then when n=1, the term  is 2. If n=2, the term  is 6. If n=3, the term  is 12, etc...
So we have this set up
| n | 1 | 2 | 3 | 4 | 5 | 6 |
Term  | 2 | 6 | 12 | 20 | 30 | 42 |
Notice how the term 2 is equal to 1*2 (where 1 is the value of n and 2 is the next number). Also, notice how 6=2*3 (where 2 is the value of n and 3 is the next number). Furthermore, take note that 12=3*4 (where 3 is the value of n and 4 is the next number) etc....
So ANY term in this sequence can be written as 
For instance, let's say that  . This would mean that 
So when  , then the term is 12
Before we can wrap this up, we need to divide the expression by 2 to get  . Why? Because we multiplied every term of the original sequence by 2. So we need to divide by 2 to get back to the original expression.
So the formula for the sequence 1,3,6,10,15,21 is 
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