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Bismuth83
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 09 Oct 2024, 17:00
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k: 6 \(a_k\): 26
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15% (low)

Question Stats:

87% (01:29) correct 13% (02:00) wrong based on 1020 sessions

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In a particular sequence, \(a_1 = 2\), \(a_2 = 4\), and \(a_n= (a_{n-1}) + (a_{n-2})\). For a particular positive integer k, which could be the pair of k and \(a_k\)?
k \(a_k\)
5
6
10
12
18
26
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J_21
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 10 Oct 2024, 00:15
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can anyone explain why answer is not 6,18 here ??
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pintukr
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 10 Oct 2024, 11:27
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Given,

an = (an - 1) + (an-2)

So,
a1 = 2
a2 = 4
a3 = 4 + 2 = 6
a4 = 6 + 4 = 10
a5 = 10 + 6 = 16
a6 = 16 + 10 = 26
a7 = 26 + 16 = 42...and so on .

So, 1st Blank = 6
2nd Blank = 26
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 10 Oct 2024, 17:00
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1. We are given a sequence of positive whole numbers and are asked what could be a possible \(k\), \(a_k\) pairing.

2. The possible values for \(a_k\) aren't large, so we can just list a few terms:

(2) (4) (2 + 4) (4 + 2 + 4) (2 + 4 + 4 + 2 + 4) (4 + 2 + 4 + 2 + 4 + 4 + 2 + 4) .... \(\rightarrow\) 2 4 6 10 16 26 ....

3. 6, 10 and 26 pop up as answers. They are \(a_3\), \(a_4\), and \(a_6\), respectively. The only \(k\) that works is 6.

4. So, our answer is \(k = 6\), \(a_k = 26\).
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 02 Nov 2024, 06:08
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a1 = 2,
a2 = 4,
a3 = 6,
a4 = 10,
a5 = 16,
a6 = 26.

So (6,26)
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 10 Feb 2025, 03:54
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This is the long method , is there any shortcut for this problem ?
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 18 May 2025, 03:24
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It's basically the sum of previous 2 terms. You just need to hit and try for K=5 and 6 and it won't take more than 30 seconds to get to the correct answer.
seleniumOxide
This is the long method , is there any shortcut for this problem ?
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In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2). 18 May 2025, 07:42
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Solution:

Given in the question stem:

1. \(a_1\) = 2

2. \(a_2\) = 4

3. \(a_n\)= (\(a_{n-1}\)) + (\(a_{n-2}\))(By using this formula we can get to the solution)

\(a_3\) = (\(a_{n-1}\)) + (\(a_{n-2}\))= 4 + 2 = 6

\(a_4\) = 6+4 = 10

\(a_5\) = 10+6 = 16

\(a_6\) = 16+10= 26

Hence, the only choices that pair with K and \(a_k\) are 6 and 26.
Bismuth83
In a particular sequence, \(a_1\) = 2, \(a_2\) = 4, and \(a_n\)= (\(a_{n-1}\)) + (\(a_{n-2}\)). For a particular positive integer k, which could be the pair of k and \(a_k\)?
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