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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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18 May 2013, 00:25
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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 $$a_1-1$$ 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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18 May 2013, 00:37
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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 $$a_1-1$$ 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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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.

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.

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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, 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.

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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, 03:40
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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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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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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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30 Oct 2014, 01:52
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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.

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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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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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.

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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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