Difficulty comprehending geometric sequences

[LauraS862]

Hi, Even after reading the explanation, I'm still having trouble understanding this question (#22) from the MGMAT Formulas, Functions and Sequences Drill Worksheet.

Problem 22
In a certain sequence, the term a(n) is given by the formula a(n) = 2 x a (n-1) where a1 = 1. What is the positive difference between the sum of the first ten terms of the sequence and the sum of the 11th and 12th terms of the same sequence?

A) 1
B) 1024
C) 1025
D) 2048
E) 2049

Looking at the answers, it was logical to me that we could eliminate A as it is fairly reasonable that while it will factor into the answers, it most likely isn't the right one. Seeing A, I narrowed the answers down to C and E as I suspected while A wasn't correct, there would be a catch remembering a value of 1 some where...

Also, after writing out the first couple of terms, I was able to recognize that the sequence was actually a(n) = 2^(a(n-1)).

So I got to...
(2^10 + 2^11) - (2^9 + 2^8 + 2^7...) and got stuck here. Wasn't sure how to solve it from here. Can you help?

[PetriF258]

I have seen that when one has to work with sum of a geometric term, it helps to list the first few items and see whether there is a sequence:

a1 = 1
a2 = 2 sum:3
a3 = 4 sum:7
a4 = 8 sum:15
a5 = 16 sum:31

at this point you should notice that sum of all terms to an = 2^n - 1; for example sum up to a4 = 2^4 - 1 = 15; a5 = 2^5 - 1 = 31.

Therefore the sum of the first 10 terms is equal to 2^10 - 1 = 1023 and the answer should then be (1024 (a11) + 2048 (a12)) less 1023 equals 2049; is this the correct answer?

[RonPurewal]

please re-post this query in the correct folder (MGMAT non-CAT math folder).

thanks.