1,3,6,10,15

whats the 15th and 30th term

Question

1,3,6,10,15

whats the 15th and 30th term

campbell_st · Answer

looks like the set of triangular numbers

$$a_{n} = a_{n -1} + n$$

anonymous · Answer

@campbell_st what? im so confused..

campbell_st · Answer

the sequence is well know.... like the set of square numbers... 

you can draw a triangle with numbers

|dw:1377719816292:dw|

the sequence is increasing by the counting numbers1, 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10... 

so the 6th number is 15 + 6 = 21    7th = 21 + 7 = 28

so the formula for a term is 

$$a_{n} = \frac{n(n + 1)}{2}$$

check to see if the formula fits... if it does then its easy to find the 15th and 30th numbers in the sequence