The first term of a sequence is -2 and the second term is 2. Each

Question

The first term of a sequence is -2 and the second term is 2. Each subsequent odd term is found by adding 2 to the previous term, and each subsequent even terms is found by multiplying the previous term by -1. What is the sum of the first 669 terms?

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct solution.

A. -4
B. -2
C. 0
D. 2
E. 4

Kudos for a correct  solution .

KS15 · Accepted Answer

The sequence of terms is -2,2,4,-4 and this continues
Since there are 669 terms, the number divisible by 4 is 668
668/4=167
So the sequence of terms will continue for 167 times in the same manner. 
Sum of each sequence=0
Sum of 668 terms=0
669th term=-2
Answer B

ENGRTOMBA2018 · Answer

a_1 = -2
a_2 = 2
a_3 = 4
a_4 = -4 
a_5 = -2 ...., thus the 'cyclicity' of this pattern is 4. The nearest multiple of 4 to 669 is 668. The sume of any pair of 4 terms = 0. Thus the sum of the first 668 terms = 0.

669th term = -2 and thus the sum of the first 669 terms = 0-2=-2. B is the correct answer.

D3N0 · Answer

Ans:B

Solution: from the statement we can find the sequence. Which is { -2,2,4,-4,-2,2,-4,4..... }
its repetitive sequence of 4 elements and sum of those four elements (first four terms) is 0
sum of 669 terms = 668+1 terms = 0 +( -2) = -2

Temurkhon · Answer

-2,2,4,-4

so cyclicity is 4. 669=167*4+1, where 1 is remainder. Means that 669th term is -2. Their sum is 0+(-2)=-2

B

Bunuel · Answer

GROCKIT OFFICIAL SOLUTION:

Clearly, we are not looking to enter all 669 terms and see what the last one is. But, we can do a few and check out the pattern.

n = 1,  a_n = -2

n = 2,  a_n = 2

n = 3,  a_n = 4

n = 4,  a_n = -4

n = 5,  a_n = -2

n = 6,  a_n = 2

Since we can see that the pattern will repeat every 4 terms, we can solve for the remainder after dividing 669/4. Since 4 goes into 668 evenly, we know that the value will be equivalent to that of the first term, which = -2.

LATIFA221B · Answer

Q1 = -2 
Q2 = 2
Q3 = 4
Q4 = -4 
Q5 = -2 
Q6 = 2
 Q7 = 4 
Q8 = -4 
Q9 = -2

each group of 4 numbers yield to a sum of 0 
669/4 = 167 and the reminder is 1. 
sum = 0*167+ -2 = -2

Kinshook · Answer

Given: 
1. The first term of a sequence is -2 and the second term is 2. 
2. Each subsequent odd term is found by adding 2 to the previous term, and each subsequent even terms is found by multiplying the previous term by -1.

Asked: What is the sum of the first 669 terms?

a1 = -2
a2 = 2
a3 = 4
a4 = -4
a5 = -2
a6 = 2
a7 = 4
a8 = -4

The pattern {-2,2,4,-4} repeats after every 4 terms and sum of -2+2+4-4 = 0

669 = 4*167 + 1
sum of 167 such sequences of {-2,2,4,-4} will be 0.
a669 = a1 = -2

IMO B

CrackverbalGMAT · Answer

In this question, it may seem at the start that this question will take a lot of time to solve since we have to find the sum of 669 terms. 
But, if you are able to establish a pattern, you will be able to work with this much faster.

Given that  t_1  = - 2 and  t_2  = 2. Also,  t_3  = 4,  t_4  = -4,  t_5  = -2,  t_6  = 2,  t_7  = 4 and  t_8  = -4.

From the above, we can see clearly that the terms are repeating in a cyclic manner with a cyclicity of 4. Also, we see that, in every cycle, the sum of the terms in that cycle is ZERO. 
All that is left now is to see how many cycles are required to get closer to 669 terms.

The divisibililty rule for 4 says that the last 2 digits of the number should form a number divisible by 4. 69 is the number formed by the last 2 digits of 669. 
69 is not divisible by 4 and leaves a remainder of 1 when divided by 4. This means that we will have the 1st term of the cycle left out.

669 = 167 * 4 + 1. This means there will be 167 cycles and the 1st term of the 168th cycle left out.

The sum of the terms in the 167 cycles is ZERO. The first term of any cycle is -2. Therefore the sum of the first 669 terms = -2.

The correct answer option is B.

Hope this helps!

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.

The first term of a sequence is -2 and the second term is 2. Each

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

The first term of a sequence is -2 and the second term is 2. Each

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