SAT Math Challenge Problem

Series of numbers Sometimes the SAT will ask you to notice a pattern in a sequence of numbers. -3, -1, 1, 3, 5 These numbers form what are known as a sequence. The one above is known as an arithmetic sequence, because each number increases by a fixed sum. So if we were to continue the sequence, we would start with 7, continuing to add by two (†¦7, 9, 11, 13†¦). The little dots (†¦), by the way, mean that numbers came before (as in the case of ‘7’) or after (as in the case of ‘13’). Now for a slightly trickier series: 2, 4, 8, 16, 32†¦256 Okay, that’s actually not that difficult either—each number is increasing by (x2). Notice, I’m not adding by a fixed number, the way I was doing above. When you multiply by a fixed number, you get a geometric sequence. Remember the dots just mean that you don’t write out all of the numbers, though the pattern continues. With this sequence, instead of writing 64, 128, and 256, I just replace them with dots and end with 512, which is the last number in the sequence. Now that you’ve got the basics, let’s take it up a few notches. Drum roll please: It’s the Challenge Problem! Challenge Problem -1/128, 1/32, -1/8, 1/2†¦2048 In the sequence above, how many values are less than -1? (A)  Ã‚  Ã‚   Zero (B)  Ã‚  Ã‚   Two (C)  Ã‚  Ã‚   Three (D)  Ã‚   Five (E)  Ã‚  Ã‚   Six The first thing to remember is that -1/128 and -1/8 are not less than -1. On a number line, they will both fall to the right of -1, because they are both closer to zero, and thus greater than -1. Of course a challenge problem wouldn’t be that straightforward, where all you have to do was count the numbers provided. In this case, there are a few missing numbers, which are key to getting this right. To figure out these numbers, we have to unlock a pattern. Can you figure out what it is, and what the actual answer is (Hint: It’s not (B)!). Leave a comment with your work and your answer, or let me know if you get stuck!