# Math Help - recursive formula

1. ## recursive formula

Hiya I need give a recursive formula for the numbers 1,3,6,10,15,21,34

I found an+1=an+2n+1

Is this right?, and if it isnt what did i do wrong

I also need to give a formula for n in the number series but that excapes me, any ideas or clues would be helpful, Thanks

2. Originally Posted by JBswe
Hiya I need give a recursive formula for the numbers 1,3,6,10,15,21,34

I found an+1=an+2n+1

Is this right?, and if it isnt what did i do wrong

I also need to give a formula for n in the number series but that excapes me, any ideas or clues would be helpful, Thanks
Obviously it's not right - a simple substitution of values of n reveals that in short order.

Observe the pattern:

$a_2 - a_1 = 3 - 1 = 2$

$a_3 - a_2 = 6 - 3 = 3$

$a_4 - a_3 = 10 - 6 = 4$

Clearly:

$a_n - a_{n-1} = n$

Therefore:

$a_{n+1} - a_n = n + 1 \therefore a_{n+1} = a_n + n + 1$, where $a_1 = 1$. The coefficient of n is 1, NOT 2.

$a_{n+1} - a_n = n + 1$ is a recurrence relation - there are standard techniques for solving $a_n$ in terms of n ......