Find a formula for 1, 3, 6, 10, 15, 21,

[annoymage]

Homework Statement

find the formula for

1,3,6,10,15,21,...

Homework Equations

n/a

The Attempt at a Solution

i only can find n>=3

Tn = 3 + \sum i ; i=3 to n

help T_T

 

[mg0stisha]

For one thing, the numbers in the way you listed them are called a sequence. Do you see a pattern among those numbers? That may help you.

 

[annoymage]

yea lol, it's sequence ;P sorry, and yea, i saw the pattern, but only start from 3 T_T

 

[HallsofIvy]

Homework Statement

find the formula for

1,3,6,10,15,21,...

Homework Equations

n/a

The Attempt at a Solution

i only can find n>=3

Tn = 3 + \sum i ; i=3 to n

But 3= 1+ 2 and 1= 0+ 1 so you can say it is T_n= \sum_{i= 1}^n i That's a well known sum with a well known formula. Look up "triangular numbers".

help T_T

 

[annoymage]

thanks, how come i didn't realized it's T_n= \sum_{i= 1}^n i instead of Tn = 3 + sum(i) ; i=3 to n.

thank you :D

 

[gomunkul51]

There is no sigma notation in sequences, a sequence is written as:

<br /> \left \{a_{n} \right \}_{n=0}^{N}<br />

as to your sequence it could be defined by a recursive formula:

<br /> a_{n+1}=a_{n}+n+2<br />

<br /> a_{0}=1<br />