It is currently 14 Aug 2020, 09:51

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Sequence S is defined as follows: S 1 = 2

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 12642
Followers: 269

Kudos [?]: 3178 [0], given: 11677

Sequence S is defined as follows: S 1 = 2 [#permalink]  25 Jul 2020, 09:56
Expert's post
00:00

Question Stats:

90% (01:00) correct 9% (00:00) wrong based on 11 sessions
Sequence S is defined as follows:$$S_1 = 2, S_2=2^1, S_3=2^2,......, S_n=2^{n-1}$$. What is the sum of the terms is sequence S when $$n=10$$ ?

A. $$2^9$$

B. $$2^{10}$$

C. $$2^{16}$$

D. $$2^{35}$$

E. $$2^{37}$$
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Intern
Joined: 25 Jul 2020
Posts: 30
Followers: 0

Kudos [?]: 14 [1] , given: 2

Re: Sequence S is defined as follows: S 1 = 2 [#permalink]  25 Jul 2020, 10:55
1
KUDOS
The question has a bug. You mention that Sn = 2^(n - 1), but from your description the first term is 2, which is 2^1, not 2^0. And also there isn't quite any correct answer either, because

S_n = a(r^n - 1)/(r - 1). Then S_n = 2(2^n - 1) or (2^n - 1) depending on what a is, and I don't think any of the options fit it.

Edit: missed that the first term is 2, not 1, welp. Answer is $$2^10$$ then.

Last edited by Leaderboard on 27 Jul 2020, 11:03, edited 1 time in total.
Manager
Joined: 02 May 2020
Posts: 90
Followers: 1

Kudos [?]: 67 [0], given: 14

Re: Sequence S is defined as follows: S 1 = 2 [#permalink]  26 Jul 2020, 09:32
The question has a bug. You mention that Sn = 2^(n - 1), but from your description the first term is 2, which is 2^1, not 2^0. And also there isn't quite any correct answer either, because

S_n = a(r^n - 1)/(r - 1). Then S_n = 2(2^n - 1) or (2^n - 1) depending on what a is, and I don't think any of the options fit it.

When n=10

S = S_1 + S_2 + .... + S_9 + S_10

=> S = 2 + 2^1 + 2^2 + 2^3 + .... + 2^8 + 2^9
=> S - 2 = 2^1 + 2^2 + 2^3 + .... + 2^8 + 2^9

Lets consider RHS as X

X = 2^1 + 2^2 + 2^3 + .... + 2^8 + 2^9
2*X = 2^2 + 2^3 + .... + 2^8 + 2^9 + 2^10

subtract first equation from second

=> 2*X - X = -2^1 + 0 + 0 + 0 + .... + 0 + 0 + 2^10
=> X = 2^10 - 2

S = X + 2 = 2^10

It would have been better if it was mentioned that S_n = 2^(n-1) for n>1.
Intern
Joined: 15 Mar 2020
Posts: 16
Followers: 0

Kudos [?]: 14 [0], given: 7

Re: Sequence S is defined as follows: S 1 = 2 [#permalink]  27 Jul 2020, 11:02
Sum = 2^9 +2^8 +... + 2^2 + 2^1 + 2
Sum = 2(2^8 + 2^7 + ... +2 + 1 + 1)
Sum = 2^2(2^7 + 2^6 + ... + 2^1 + 1 + 1) ...
Sum = 2^10
Re: Sequence S is defined as follows: S 1 = 2   [#permalink] 27 Jul 2020, 11:02
Display posts from previous: Sort by