series one

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series one

by GmatTakerNo.1 » Mon May 03, 2010 8:06 am
I think the solution is easy, but I´m missing the last thought to solve it.

9. If the sequence x1, x2, x3, ..., xn, ... is such that x1 = 3 and xn+1= 2xn - 1 for n ≥ 1, then x20 - x19 equals?
a) 219
b) 220
c) 221
d) 220 - 1
e) 221 - 1


The answer is A. Maybe you can help me with this one.
Source: — Problem Solving |

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by susantaiitk » Mon May 03, 2010 8:18 am
i got by this way:

series = 3 , 5, 9, 17, 33, ....
diff = 2, 4, 8, 16, ... 2^n

So X19 = 3 + (2 + 4 + 8 + 16 ... +2^18)
X20 = 3 + (2 + 4 + 8 + 16 ... +2^18 + 2^19)

X20 - X19 = 2^19