If the sequence x1, x2, x3, ..., xn, ... is such that x1 = 3 and xn+1 = 2xn - 1 for n ≥ 1, then x20 -
x19 =
A. 2^19
B. 2^20
C. 2^21
D. 2^20 - 1
E. 2^21 - 1
x19 =
A. 2^19
B. 2^20
C. 2^21
D. 2^20 - 1
E. 2^21 - 1
When the rule is followed, the sequence appears to be running like...roger federer wrote:If the sequence x1, x2, x3, ..., xn, ... is such that x1 = 3 and xn+1 = 2xn - 1 for n ≥ 1, then x20 -
x19 =
A. 2^19
B. 2^20
C. 2^21
D. 2^20 - 1
E. 2^21 - 1
3, 5, 9, 17, 33, ...
noticed anything?
Ist and IInd differ by 2^1, IInd and IIIrd differ by 2^2, IIIrd and IVth differ by 2^3,...and so on, to let us conclude that 19th and 20th would differ by [spoiler]2^19.
A[/spoiler]
