In a sequence a1, a2, …, each term after the first is found by taking

Question

In a sequence  a_1 , a_2 ,…, each term after the first is found by taking the negative of the preceding term, and adding 1. If  a_1 = 2 , what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101

nick1816 · Answer

First term= a_1 
Second term =  -a_1 + 1 
Third term =  a_1-1+ 1= a_1 
fourth term =  -a_1+ 1
And so on

the sum of the first 99 terms=  {49* }+a_1 = 49+2=51

Lampard42 · Answer

a1=2,a2=-1,a3=2,a4=-1....; So all odd values of n will be 2 and all even values will be -1; 50 Odd terms and 49 even terms; 50*2-49=51 IMO B

nick1816 · Answer

There are 50 odd terms and 49 even terms.

Archit3110 · Answer

from the given series we can say that odd no are 2 and even are -1
so total odd from 1 to 99 ; 50 and even ; 49
so 50*2+49*(-1) = 51
IMO C

BrentGMATPrepNow · Answer

Let's list some terms to get a better understanding of the desired sum.
 a_1 = 2 
 a_2 = -2 + 1 = -1 
 a_3 = 1 + 1 = 2 
 a_4 = -2 + 1 = -1 
 a_5 = 1 + 1 = 2 
 a_6 = -2 + 1 = -1 
.
.
.
We can see that all ODD numbered terms are  2 , and all EVEN numbered terms are  -1

From 1 to 99 inclusive, there are  50  ODD numbered terms and  49  EVEN numbered terms

So, sum = ( 50 )( 2 ) + ( 49 )( -1 )
= 100 + (-49)
= 51

Answer: C

Cheers,
Brent

ScottTargetTestPrep · Answer

We see that a1 = 2, a2 = -2 + 1 = -1, a3 = 1 + 1 = 2, a4 = -2 + 1 = -1 and so on.

Thus we can see that the odd-numbered terms are all 2 and the even-numbered terms are all -1. Since in the first 99 terms, there are 50 odd-numbered terms and 49 even-numbered terms, then the sum of the first 99 terms is:

50(2) + 49(-1) = 100 - 49 = 51

Answer: C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a sequence a1, a2, …, each term after the first is found by taking

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a sequence a1, a2, …, each term after the first is found by taking

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards