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In a certain sequence, the term an is defined by the formula
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27 Jul 2018, 07:17
27 Jul 2018, 07:17
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Question Stats:
62% (02:23) correct
37% (02:48) wrong based on 66 sessions
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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
(A) 1
(B) 1,024
(C) 1,025
(D) 2,048
(E) 2,049
Re: In a certain sequence, the term an is defined by the formula
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12 Aug 2018, 05:35
12 Aug 2018, 05:35
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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.
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.
Re: In a certain sequence, the term an is defined by the formula
[#permalink]
19 Jul 2020, 12:05
19 Jul 2020, 12:05
Does GRE bring something like that ?
