2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

The answer is 2^9 but I have no idea how to get that quickly enough.

2+2^2+2^3....+2^8= 2(2^8-1)/(2-1)=2^9-2

2^9-2+2= 2^9

Sorry Sumit. Could you please explain how you got there? I cannot follow any of your steps :-(
Thanks,

i used the formula for sum of a Geometric progression.....which is a(r^n -1)/r-1 where a is the first term of the GP and r the multiplier.

oh great! thanks so much -steph

a couple of comments.

first: when you're looking for the key to a pattern-based problem such as this one, you should zero in on anything that is UNUSUAL in the pattern developed. in this case, there are two 2's at the beginning (versus only one of everything else), so that seems like an ideal place to start.

adding the first two terms gives 2 + 2 = 2(2) = 2^2.

now we have two 2^2's, so that's 2^2 + 2^2 = 2(2^2) = 2^3.

now we have two 2^3's, so that's 2^3 + 2^3 = 2(2^3) = 2^4.

etc.

continue this pattern all the way up to 2^8 + 2^8 = 2(2^8) = 2^9.

--

also, don't forget that this is (or at least was, until this post!) a multiple-choice problem. since the choices are likely to be widely spread apart (they're probably different powers of 2, or some other wildly varying quantities), you can ESTIMATE the answer if you think figuring it out will take too much time.
to wit:
start with the big stuff: 2^8 = 256, 2^7 = 128, 2^6 = 64, 2^5 = 32.
if you add up all this stuff, you have 480, so you can confidently say that the answer is "a lil more than 480" (because the rest of the terms are really small numbers).

if you're going to do this, it helps to have memorized the powers of 2 - something you should do anyway, with the assistance of flash cards. you should not have to waste time calculating the different powers of 2; you should just have them memorized, up to 2^10 or so.