SOLUTION: 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

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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