PS

[ukr.net]

If the sequence X(1), X(2), X(3),...,X(n),..is such that X(1) = 3 and X(n+1) = 2X(n) - 1 for n = 1, then X(20)-X(19) =

2^19
2^20
2^21
2^20 - 1
2^21 - 1

The ANS is A ,but how to solve it?

[Suyog]

x(2) = 2(x(1)) -1 = 2(3) -1 = 5

As per the series...

x(1) = 2^1 + 1
x(2) = 2^2 + 1 and so on

so,
x(19) = 2^19 + 1 and
x(20) = 2^20 + 1

x(20) - x(19) = (2^20 + 1) - (2^19 + 1)
= 2^20 + 1 - 2^19 - 1
= 2^20 - 2^19
= 2^19

Ans A

[samirpandeyit62]

As per the series...

x(1) = 2^1 + 1
x(2) = 2^2 + 1 and so on

&

x(20) - x(19)

= 2x(19 ) - 1 - x(19) = x(19) -1

so reqd val is 2^19 -1 + 1 = 2^19