In a certain sequence, the term \(a_n\) is defined by the formula...

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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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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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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