In a certain sequence, the term $a_n$ is defined by the formula...

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BTGmoderatorLU: Moderator; Posts: 2575; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Feb 04, 2020 9:06 am

Source: Manhattan Prep

In a certain sequence, the term $a_n$ is defined by the formula $a_n = 2\cdot a_{n-1}$ for each term $n \geq 2$. If $a_1=1$, what is the positive difference between the sum of the first 10 terms s of the sequence and the sum of the 11th and 12th terms of the same sequence?

A. 1
B. 1,024
C. 1,025
D. 2,048
E. 2,049

The OA is E

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Source: Beat The GMAT — Problem Solving | Tue Feb 04, 2020 9:06 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: In a certain sequence, the term $a_n$ is defined by the formula...

by deloitte247 » Sat Feb 08, 2020 1:14 am

Sum of the first 10 terms
$$s=2^0+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9$$

Where each term is gotten from $$2^{n-1}$$
s= 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512
s=1023

Difference between s and sum of 11th and 12th term = 3072 - 1032 = 2049
Answer = E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In a certain sequence, the term $a_n$ is defined by the formula...

by Scott@TargetTestPrep » Sat Feb 08, 2020 7:17 pm

BTGmoderatorLU wrote: ↑
Tue Feb 04, 2020 9:06 am
Source: Manhattan Prep

In a certain sequence, the term $a_n$ is defined by the formula $a_n = 2\cdot a_{n-1}$ for each term $n \geq 2$. If $a_1=1$, what is the positive difference between the sum of the first 10 terms s of the sequence and the sum of the 11th and 12th terms of the same sequence?

A. 1
B. 1,024
C. 1,025
D. 2,048
E. 2,049

The OA is E

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