sequence

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beater: Master | Next Rank: 500 Posts; Posts: 301; Joined: Tue Apr 22, 2008 6:07 am; Thanked: 2 times

by beater » Mon Sep 22, 2008 11:52 am

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?

A. 2^18
B. 3(2^17)
C. 7(2^16)
D. 3(2^16)
E. 7(2^15)

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Source: Beat The GMAT — Problem Solving | Mon Sep 22, 2008 11:52 am

jeenashiva: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Wed Sep 17, 2008 12:10 pm; Location: Atlanta, USA; GMAT Score:480

by jeenashiva » Mon Sep 22, 2008 12:03 pm

I will go with E.7(2 ^15).

What is the OA?

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gmat579: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Sep 15, 2008 5:14 pm; Thanked: 2 times; GMAT Score:740

by gmat579 » Mon Sep 22, 2008 12:47 pm

The sequence 1, 2, 4, 8, 16, 32, …, can be written as

2^0, 2^1, 2^2, 2^3,...

16th term is 2^15
17th term is 2^16
18th term is 2^17

Adding these - 2^15 + 2^16 + 2^17

= 1*2^15 + 2^1*2^15 + 2^2*2^15
= (1 + 2 + 4) 2^15
=7*2^15
Answer is E.

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beater: Master | Next Rank: 500 Posts; Posts: 301; Joined: Tue Apr 22, 2008 6:07 am; Thanked: 2 times

by beater » Mon Sep 22, 2008 12:52 pm

Thanks guys! OA - E

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pre-gmat: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue Jul 15, 2008 7:03 pm; Thanked: 5 times

by pre-gmat » Mon Sep 22, 2008 1:05 pm

isnt this a geometric sequence?

what if we apply formula...

Sn = a1(1-r^n)/ 1-r

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Thu Sep 25, 2008 1:55 am

pre-gmat wrote:isnt this a geometric sequence?

what if we apply formula...

Sn = a1(1-r^n)/ 1-r

the above formula is for the sum of 1st n terms, we want only the sum of the 16th, 17th and the 18th term

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