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# In a certain sequence, the term an is defined by the formula

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1601 [0], given: 373

In a certain sequence, the term an is defined by the formula [#permalink]  27 Jul 2018, 07:17
Expert's post
00:00

Question Stats:

33% (01:37) correct 66% (00:45) wrong based on 3 sessions
In a certain sequence, the term an is defined by the formula $$a_n = 2 \times a_{n - 1}$$ for each integer n ≥ 2. If $$a_1 = 1$$, what is the positive difference between the sum of the first 10 terms 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
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1601 [0], given: 373

Re: In a certain sequence, the term an is defined by the formula [#permalink]  12 Aug 2018, 05:35
Expert's post
Explanation

This is a geometric sequence: each new number is created by multiplying the previous number by 2.

Calculate the first few terms of the series to find the pattern: 1, 2, 4, 8, 16, and so on.

Geometric sequences can be written in this form: $$a_n = r^{n – 1}$$, where r is the multiplied constant and n is the number of the desired term. In this case, the function is $$a_n = 2^{n – 1}$$.

The question asks for the difference between the sum of the first 10 terms and the sum of the 11th and 12th terms. While there is a clever pattern at play, it is hard to spot. If you don’t see the pattern, one way to solve is to use the calculator to add the first ten terms: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1,023.

The 11th term plus the 12th term is equal to 1,024 + 2,048 = 3,072. Subtract 1,023 to get 2,049.
_________________

Sandy
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Re: In a certain sequence, the term an is defined by the formula   [#permalink] 12 Aug 2018, 05:35
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