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The sequence of four numbers a1, a2 , a3 and a4 is such that

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The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]

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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 \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

(1) \(a_2=15\)

(2) \(a_4 = 29\)
[Reveal] Spoiler: OA

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

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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 \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?


\(a_n=a_{n-1}+(a_1-1)\)

1. \(a_2=15\)
\(a_2=a_{1}+(a_1-1)\)
\(15=2a_{1}-1\)
\(a_1=8\)
Sufficient

2. \(a_4 = 29\)
From the main formula above we can write \(a_4\) as \(a_4=a_{1}+3(a_1-1)\)
\(29=a_{1}+3(a_1-1)\)
\(29=4a_{1}-3\)
\(a_1=8\)
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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New post 18 May 2013, 04:10
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 \(a_1-1\) 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 => 4a1-3 = 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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New post 19 May 2013, 03:35
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 \(a_1-1\) 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 \(a_n = a_{n-1} + (a_1 - 1) = na_1 - (n - 1)\)

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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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 \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

1. \(a_2=15\)

2. \(a_4 = 29\)


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if-a1-a2-a3-an-is-a-sequence-such-that-an-2n-129753.html
an-infinite-sequence-of-positive-integers-is-called-a-127696.html

Hope it helps.
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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]

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New post 29 Oct 2014, 20:19
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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alexa wrote:
Bunuel please solve this question, I don't understand the solution for statement #2.

Thank you!


The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

Each number after the first is \(a_1-1\) greater than preceding number means that:
\(a_2=a_1+(a_1-1)=2a_1-1\)
\(a_3=a_2+(a_1-1)=3a_1-2\)
\(a_4=a_3+(a_1-1)=4a_1-3\)

(1) \(a_2=15\). We can find \(a_1\). Sufficient.

(2) \(a_4 = 29\). We can find \(a_1\). Sufficient.

Answer: D.

Hope it's clear.
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The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]

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New post 12 Nov 2015, 03:25
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 \(a_1-1\) 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
\(a_2\) = \(a_1\) + \(a_1-1\) - (i)
\(a_3\) = \(a_1\) + 2\(a_1-1\) - (ii)
\(a_4\) = \(a_1\) + 3\(a_1-1\) - (iii)

Required: \(a_1\) = ?

Statement 1: \(a_2=15\)
Using (i) we can find the value of \(a_1\)
SUFFICIENT

Statement 2: \(a_4 = 29\)
Using (iii), we can find the value of \(a_1\)
SUFFICIENT

Hence 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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New post 22 Oct 2017, 02:10
Nth term in AP is denoted as tn=a+(n-1)d .

(1) says, 15=a1+(4-1)(a1-1) => 15=a1+3(a1-1) , from this a1 can be found. SUFFICIENT.

(2) says, 29=a1+(4-1)(a1-1) => 29=a1+3(a1-1) , from this a1 can be found. SUFFICIENT.

Thus answer D.

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Re: The sequence of four numbers a1, a2 , a3 and a4 is such that   [#permalink] 22 Oct 2017, 02:10
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