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The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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18 May 2013, 01:25
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The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_11\) greater than preceding number . What is the value of \(a_1\)? (1) \(a_2=15\) (2) \(a_4 = 29\)
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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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18 May 2013, 01:37
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The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_11\) greater than preceding number . What is the value of \(a_1\)?\(a_n=a_{n1}+(a_11)\) 1. \(a_2=15\)\(a_2=a_{1}+(a_11)\) \(15=2a_{1}1\) \(a_1=8\) Sufficient 2. \(a_4 = 29\)From the main formula above we can write \(a_4\) as \(a_4=a_{1}+3(a_11)\) \(29=a_{1}+3(a_11)\) \(29=4a_{1}3\) \(a_1=8\) Sufficient D
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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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18 May 2013, 05:10
pritishmohan wrote: The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_11\) greater than preceding number . What is the value of \(a_1\)?
1. \(a_2=15\)
2. \(a_4 = 29\) given: a2  a1 = a1  1 => a2 = 2a1  1 similarly we can get a3 = 3a1  2 and a4 = 4a1  3. AD/BCE statement 1: a2 = 15 => 2a1  1 = 15.So we can get the value of a1. A alone is sufficient BCE out. statement2: a4 = 29 => 4a13 = 29 .So we can get the value of a1. B alone is sufficient. Answer is D
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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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19 May 2013, 04:35
pritishmohan wrote: The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_11\) greater than preceding number . What is the value of \(a_1\)?
1. \(a_2=15\)
2. \(a_4 = 29\) From the given information, we know that \(a_n = a_{n1} + (a_1  1) = na_1  (n  1)\) 1. \(a_2 = 15\) > \(a_2 = a_1 + (a_1  1) = 2a_1  1\) > \(2a_1  1 = 15\) > \(2a_1 = 16\) > \(a_1 = 8\) Sufficient. 2. \(a_4 = 29\) Now, \(a_4 = 4a_1  3\) > \(4a_1  3 = 29\) > \(4a_1 = 32\) > \(a_1 = 8\) Sufficient. Correct answer is D.



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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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19 May 2013, 04:40



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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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29 Oct 2014, 21:19
Bunuel please solve this question, I don't understand the solution for statement #2.
Thank you!



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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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30 Oct 2014, 02:52
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The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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12 Nov 2015, 04:25
pritishmohan wrote: The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_11\) greater than preceding number . What is the value of \(a_1\)?
(1) \(a_2=15\)
(2) \(a_4 = 29\) Given: \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) and \(a_2\) = \(a_1\) + \(a_11\)  (i) \(a_3\) = \(a_1\) + 2\(a_11\)  (ii) \(a_4\) = \(a_1\) + 3\(a_11\)  (iii) Required: \(a_1\) = ? Statement 1: \(a_2=15\) Using (i) we can find the value of \(a_1\) SUFFICIENTStatement 2: \(a_4 = 29\) Using (iii), we can find the value of \(a_1\) SUFFICIENTHence Option D Note: You do not need to solve for the values of \(a_1\). This can save precious time on the test.



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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
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22 Oct 2017, 03:10
Nth term in AP is denoted as tn=a+(n1)d .
(1) says, 15=a1+(41)(a11) => 15=a1+3(a11) , from this a1 can be found. SUFFICIENT.
(2) says, 29=a1+(41)(a11) => 29=a1+3(a11) , from this a1 can be found. SUFFICIENT.
Thus answer D.




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