## 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)    Zero

(B)    Two

(C)    Three

(D)   Five

(E)    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)!).

Chris Lele is the GRE and SAT Curriculum Manager (and vocabulary wizard) at Magoosh Online Test Prep. In his time at Magoosh, he has inspired countless students across the globe, turning what is otherwise a daunting experience into an opportunity for learning, growth, and fun. Some of his students have even gone on to get near perfect scores. Chris is also very popular on the internet. His GRE channel on YouTube has over 8 million views.

You can read Chris's awesome blog posts on the Magoosh GRE blog and High School blog!

### 4 Responses to “SAT Math Challenge Problem”

1. HSC>SAT says:

Hey, thanks for putting the time into this

Worked this out

the ratio is -4 knowing this you just use the formular a(-4)^n-1

where a=-2 because 1/2 . -4= -2

then find n using logs which gives you 6

you know that half of the numbers will be negative cause even power of -4 makes a positive term and odd powers of -4= even term

• Chris Lele says:

I follow you on most of that, but you didn’t quite get to the answer. So I want to say “good job”, but to be sure, what would you say your final answer is?

2. Abhishek says:

The answer is C (3 terms)

• Chris Lele says:

Good job, Abhishek! That’s the answer 🙂

Magoosh blog comment policy: To create the best experience for our readers, we will approve and respond to comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! :) If your comment was not approved, it likely did not adhere to these guidelines. If you are a Premium Magoosh student and would like more personalized service, you can use the Help tab on the Magoosh dashboard. Thanks!