Consecutive positive integers

[AmunaGmat]

Peter is planning to save $1 this week and then save $1 more each succeeding week than he saved a week before. His goal is to save $210. Using his knowledge that the sum P of the first Q consecutive intergers is P=Q(Q+1)/2, where Q>1, he can determine that it will take him how many weeks to reach his goals.

I modified this question from GMAT focus, I hope that is fine!!

I got this question right because it was just easy to solve the quadratic equation. However, I was kinda thinking what will I have done if I was not given the formula? For sure, guess with a pinch of salt :(

I thought of this as a linear growth problem or consecutive intergers as the problem say w=1, w+1=2 w+2=3. I know all these should finally add to 210, but not in GMAT's 2 min.
In OG 12 question 157 page 174, i ignored the formular, just calculated the number of terms and the average, then multiplied

Can someone please tell me how is this formula linked with these types of questions? What does it mean, and when can i use it to my benefit.

Cheers!!

[tim]

use the formula if you think to use it and it seems appropriate. in the first case you mention, the formula will work if you solve the quadratic or you can pick numbers (not too bad an idea in this case). for problem 157, the formula can be used if you really want to, but your approach is much better. see my video explanation of question 157 in the OG Archer for more on this..