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Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #12


The sequence of numbers a1, a2, a3

The sequence of numbers a1, a2, a3, ..., an,... is defined by for each integer n ? 1. What is the sum of the first 20 terms of this sequence? (1+1/2)-1/20, (1+1/2)-(1/21+1/22), 1-(1/20+1/22), 1-1/22, 1/20-1/22

5 Explanations


Radwa Fahmy

Why by using the formula
Sn= n (a1+an) /2 (the answer is 443/66)
We don't get the same answer (value)?!

Sep 5, 2018 • Comment

Sam Kinsman

Hi Radwa,

Good question! The problem with using that formula is that it is only for arithmetic sequences. Keep in mind that arithmetic sequences are evenly spaced, and have a common difference. For example, the sequence 5, 10, 15, 20, 25 is an arithmetic sequence, where the common difference is 5. That sequence is evenly spaced.

Arithmetic sequences can be written in the form:

an = a1 + (n-1)d

The sequence we are dealing with in this practice problem is not evenly spaced, and it cannot be written in the form above. Thus, it is not an arithmetic sequence, and the formula you mentioned won't work.

You can learn more about arithmetic sequences here:

Sep 19, 2018 • Reply


Why can't we use the idea that a sum of a sequence is the number of items in the last multiplied by the average of the first and last pair? I almost got to the correct answer but then got tripped up when I thought I had to divide by 2.

Dec 17, 2017 • Comment

Sam Kinsman

Good question! That formula only works when we have arithmetic sequences (

Dec 21, 2017 • Reply


Jessica Wilson

Can we always assume in a question like this that we take the first term plus the last?

Aug 8, 2017 • Comment

Jonathan , Magoosh Tutor

Hi Jessica,
No that should not be something we assume. With a sequence, we SHOULD write out the terms looking for a pattern (if we don't see the pattern immediately) and these kind of cancellations are things we should keep in mind/be aware of. But problems will always be a little different, so it's important to figure out each problem on its own. Hope that makes sense :)

Sep 4, 2017 • Reply


Yosef Lewis

The takeaway here (for me) is to match your answer with answer choices available. The answer choices are not simplified, so neither should yours as the test taker.
On a similar note, don't do anything that's going to take a ridiculous amount of time! :P

Apr 15, 2014 • Comment

A huge trap is heading down a path that takes up a lot of time. One reason to practice a lot of questions—make the mistake now so you don't make the mistake on test day. :)

Apr 18, 2014 • Reply


Chris Lele

Oct 8, 2012 • Comment

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