sequences n serires

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

anjaligeorge1: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Wed Feb 20, 2008 6:23 pm; Thanked: 2 times

sequences n serires

by anjaligeorge1 » Tue Jun 24, 2008 4:03 pm

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

Quote

Source: Beat The GMAT — Problem Solving | Tue Jun 24, 2008 4:03 pm

sibbineni: Master | Next Rank: 500 Posts; Posts: 222; Joined: Fri Jan 04, 2008 8:10 pm; Thanked: 15 times

by sibbineni » Tue Jun 24, 2008 5:24 pm

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

Quote

beeparoo: Master | Next Rank: 500 Posts; Posts: 200; Joined: Sun Jun 17, 2007 10:46 am; Location: Canada; Thanked: 9 times

by beeparoo » Tue Jun 24, 2008 6:04 pm

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?