Tyler York

June 4, 2023

In this video, Achievable GRE course author Matt Roy explains how to solve a number sequence problem. Number sequences can look complicated on the GRE, but some simple tricks make them much more approachable.

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00:00:03 This sequence problem seems a little bit scary at the start because it asks for the sum of 25 numbers. Well the question it says more specifically, what is the sum of the 1st 25 numbers in a sequence in this sequence? OK, so the sequence goes from seven negative 3423 and then seven negative 3423. 00:00:30 And presumably it goes on like that. If you notice, there is a pattern there. Every time we get to 7, we restart the pattern. The pattern is every 5 digits. Okay, that's very important for this question. Every 5 digits we repeat. Well, it asks for the sum of the 1st 25 numbers in order to get that. 00:00:57 We should first ask ourselves, what is the sum of the 1st 5 numbers, these five, seven, negative three, -, 4, two and five, or two and three? Well, seven is cancelled out by -, 3 and -, 4, because -, 3 and -. 4 makes 7 or -, 7. So 7, -, 7 is obviously zero. That's the cancellation. 00:01:23 And then we're left with five. The sum of the first five sequence, the 1st 5 numbers in the sequence, is five. The question actually asks us for the sum of the 1st 25 numbers in the sequence. Well, if this repeats four other times, that would actually give us a total of 25 numbers in the sequence, right? 00:01:53 How many groups of five would there be? Well, obviously 25 / 5 is five, so there are five groups of five in this group of 25, or in the sequence of 25. So obviously all we have to do really is just multiply our sum of the first five by the total number of groups, which is just 25. The final answer is simply 25. 00:02:22 And that's all.

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