Given Data:

X1=3

Xn+1=2Xn-1------(1)

n=1 or n>1

if n=1 then (1) becomes

X2=6
X3=12
X4=24......So on

This is in Geometric progression so

Tn=ar^n-1

where r is the common ratio
a is the first term


X20 is calculated by the formula

X20=3*2^20-1 here a=3 (ieX1=3)-----2

similarly

X19=3*2^19-1-------3



2-3 gives

3*2^19-3*2^18====>3(2^19-2^18)==>3*2^18 on further simplify.....

I think either question or answer choices are wrong

sibbineni wrote:X1=3

X(n+1) = 2*X(n) - 1 ------ (Re-written for clarity)

X2=6 <--- Nope, should be 5
X3=12 <--- Should be 9
X4=24 <--- Should be 17

This is in Geometric progression so <--- Yes, you're right, it is.

...
I think either question or answer choices are wrong

By observing answers in the four first samples, a pattern emerges. Thus, the geometric progression is:

X(n) = 2^n + 1

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

I hope A is OA. Is it?

My bad ...
i have misunderstood the question

sibbineni wrote:My bad ...
i have misunderstood the question

Slight oversight, man. You just forgot to subtract '1' each time.

I do stuff like that too..