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

Question

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

Bunuel · Accepted Answer

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.

Zarrolou · Answer

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

SrinathVangala · Answer

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

doe007 · Answer

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.

Bunuel · Answer

Similar questions to practice: the-sequence-a1-a2-a3-an-of-n-integers-is-such-that-76926.html the-numbers-above-form-a-sequence-t1-t2-and-t3-which-is-106213.html 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.

alexa · Answer

Bunuel please solve this question, I don't understand the solution for statement #2.

Thank you!

TeamGMATIFY · Answer

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.

merajul · Answer

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.

BrentGMATPrepNow · Answer

Given : The sequence of four numbers a1, a2, a3 and a4 is such that each number after the first is a1 - 1 greater than preceding number  
  Let k = a1  
So, each term after a1 is k - 1 greater than the term before it.

So we have: 
a1 = k
a2 = k + (k - 1) = 2k - 1
a3 = 2k - 1 + (k - 1) = 3k - 2
a4 = 3k - 2 + (k - 1) = 4k - 3
 
  Target question :    What is the value of k?

Statement 1 : a2 = 15  
We already determined that a2 = 2k - 1
So, substitute 15 for a2 to get: 15 = 2k - 1
Solve:  k = 8 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : a4 = 29 
We already determined that a4 = 4k - 3
So, substitute 29 for a4 to get: 29 = 4k - 3
Solve:  k = 8 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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