1. ## triangular tile pattern

ok well the problem is i have to figure out how the step number is related to the number of tiles in the fig. and write an equation for how they are related so here are the numbers
in the first step there is one tile
in the second step there are three tiles
in the third step six tiles
in the fourth step 10 tiles
in the fith step 15 tiles
and so on

i understand that they increase by the amount in the prevoious plus the new number but i need to no how to write the equation

2. Originally Posted by pstutts17
ok well the problem is i have to figure out how the step number is related to the number of tiles in the fig. and write an equation for how they are related so here are the numbers
in the first step there is one tile
in the second step there are three tiles
in the third step six tiles
in the fourth step 10 tiles
in the fith step 15 tiles
and so on

i understand that they increase by the amount in the prevoious plus the new number but i need to no how to write the equation
This is called the "triangular sequence".
The sequence is,
a_n={n(n+1)/2}

This is true because they form the first sum of integers:
(1+2+3+...+n)
Which is in arithmetic progession and can easily be calculated of what the sum is, which is the one above.