Discussion
Let u represent the sum of the integers from 1 through 20, and let v represent the sum of the integers from 21 through 40. What is the value of v – u?
*This question is included in Nova Math - Problem Set Y: Sequences & Series, question #3
| (A) | 21 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 10/03/2012 15:37
Is it possible to use the formula for an arithmetic sequence to solve this, substituting 1 for a, 1 for d, and 20 for n for series u and 21 for a, 1 for d, and 40 for n for series v? Thank you for your help!
Posted: 10/03/2012 16:38
Kayla, you have to show me your work in order for me to say it is possible or not. In tests like this, rarely do you have to depend on formulas. For example, here you see the answer choices are pretty spread out, which indicates it is a good idea to use estimation.
The sum of integers from 1 to 20 can be estimated this way: 1 + 20, 2 + 19, 3 +18, etc. which adds up to 21 times 10 (since there are about 10 pairs), or about 200.
The sum of integers from 21 to 40 can be estimated as the sum of: 21 + 40, 22+39, ... or about 61 times 10, or about 600.
So the difference between the two sums are about 400, and there is only 1 answer which is close to (in this case the same to) our estimate.
The sum of integers from 1 to 20 can be estimated this way: 1 + 20, 2 + 19, 3 +18, etc. which adds up to 21 times 10 (since there are about 10 pairs), or about 200.
The sum of integers from 21 to 40 can be estimated as the sum of: 21 + 40, 22+39, ... or about 61 times 10, or about 600.
So the difference between the two sums are about 400, and there is only 1 answer which is close to (in this case the same to) our estimate.
Posted: 05/07/2014 18:44
Yes it's possible to use AP for getting the sums of the two series
Posted: 05/07/2014 18:44
Yes it's possible to use AP for getting the sums of the two series
Posted: 06/27/2015 13:50
I need a little more explanation please.Thank you.I calculated it to get the right answer but It took time.