Anugmat740
https://gmatclub.com/forum/there-is-a-sequence-an-for-a-positive-integer-such-that-a3-a1-a2-a4-232117.html Hi! In this question When I am putting n=1, I am getting answer as 2p. But for values greater than 1, I am getting answer as 4p. Can anybody help?
Hey!
I'm a new "expert" to this site looking to help students. Hopefully, I can help you.
The following is the optimal approach.
(Although there are multiple ways to solve a problem, it's important to use the fastest given that time is such a big factor on the GMAT. If you end up using a slow method, it's almost as bad as getting the question wrong because you end up wasting time.)
When you approach sequence problems, the key is usually to figure out how the sequence changes at each step (aka the pattern). The first thing to test for is simple addition or subtraction. The 2nd thing is to see if each changes by a multiplication or division. If it's not one of these, you would need to look for hints on what it could be. It could be anything!
In this specific question, you're not given actual numbers, so the best thing is to input some simple numbers so you can identify a pattern. I would start with 1. The sequence would then be 1, 2, 3, 6, 12..
As you write down the numbers, you should notice that every term doubles the last. Why? It doubles because the previous term was the sum of everything that came before it. So, when you add those 2 together, you're effectively doubling the previous term.
As a result, if a(n) = p, then a(n+1) = 2p and a(n+2) = 4p.
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However, you inquired about why you couldn't solve the problem when a(1)=p.
The thing about sequences is that the formula frequently doesn't apply to the first few terms. This is because you need a few terms to "start" the sequence.
As a result, notice how they define a(n) = a(1) + a(2)... This means that a(n) can't be a(1) or a(2).
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The key to doing well on the GMAT is not necessarily getting the right answer. It's about using the right method as this will, in turn, help you get the right answer in the fastest time.
So try using the approach that I suggested when doing sequences. Do a few more sequence problems, so you build up "muscle" memory.
Also, you should review the formulas for sum of an arithmetic and geometric progression. You don't need to memorize it, but you should know how they generally work.