Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can anyone please tell me what would be the fastest way to find the average of all numbers from $1$ to $100$ that end in $2$?

share|cite|improve this question
Evidently, the fastest way is to ask on this website. 2 answers so far in under 4 minutes. – Gerry Myerson May 22 '12 at 1:40

The numbers are of the form $10k+2$ where $k \in \{0,1,2,\ldots,9\}$. Hence, the average is $$\frac{\displaystyle \sum_{k=0}^{9} (10k+2)}{\displaystyle \sum_{k=0}^{9} 1} = 47$$ A quick way is to notice that the numbers are in arithmetic progression and hence the average is $$\dfrac{\text{First term}+\text{Last term}}{2} = \dfrac{2+92}{2} = 47$$

share|cite|improve this answer
Thanks that helped. Forgot about AP formula – Rajeshwar May 22 '12 at 1:42

Group $2$ with $92$, $12$ with $82$, $22$ with $72$, $32$ with $62$, and $42$ with $52$. Each group can be further "split" into $47$ and $47$ (for example $2+92=47+47$). So the average is $47$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.