sequence/series question. PLEASE HELP!!!!

Question

What is 32nd term if given the following

 

 

 X                 Y

 

1                  1

2                  3

3                  6

4                  10

 

 

Please help!!!!. I can see that you must add all of the previous terms to get answer? for example the 4th term is 10 so once you add the third,second,and first term you will get with answer 10? Is my approach totally wrong or am I on the right path. Regardless there is no way I could come up with the answer I need because I would have to add all the number which will obvioulsy take too long. ANY HELP WILL BE GREATLY APPRECIATED> THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!:))))

 

Answer 1

Actually 32 terms is not unreasonable if you use excel :)

 

however, you may note that the answer is the sum of the digits 

so given N digits the sum is (first+last)  times (last-first)+1/2

the second part reduces to last / 2 when starting at 1.

 

1..4  1+4 *2 

        5*2

        10

 

1..32 1+32 * 16

33 * 16

528