Monday, November 30, 2009

An Important Sequence & a CR link

Here's a type of Sequences question I wasn't aware of, till now.

Repeating Patterns

Many times, repeating patterns will yield a remainder question.
The first term of a sequence is  -2 and the second term is 2. Each subsequent odd term is found by adding 2 to the previous term, and each subsequent even terms is found by multiplying the previous term by -1. What is the sum of the first 669 terms?

Clearly, we are not looking to enter all 669 terms and see what the last one is. But, we can do a few and check out the pattern.
n = 1, a_n = -2
n = 2, a_n = 2
n = 3, a_n = 4
n = 4, a_n = -4
n = 5, a_n = -2
n = 6, a_n = 2
Since we can see that the pattern will repeat every 4 terms, we can solve for the remainder after dividing 669/4. Since 4 goes into 668 evenly, we know that the value will be equivalent to that of the first term, which = -2.

Also discovered a whole host of useful GMAT CR articles on BTG. Read the first two (in chronological order) and found them pretty useful. Even assumptions are of two types: sufficient and necessary! And the question type (by a subtle change in wording) can change the answer! Damn. Those 2 are definite re-read material.

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