If an = -1n, what is the sum of all possible values of an if n is any

Question

If  a_n = (-1)^n , what is the sum of all  a_n  if  n  is any integer from  1  to the  60 th prime number?

(A) -2

(B) -1

(C) 0

(D) 1

(E) 2

Source:  Marty Murray Coaching

u2409 · Answer

So starting with -1 the sequence adds up to 0 if it ends with even number and -1 if odd.
As 61st prime is odd (as all primes are, except 2), the sequence will add up to -1.

hejwej · Answer

Am i misinterpreting what ADD means? is the question not asking us to: -1+1+(-1)+(-1)+(-1).....= ???

gmatnoob24 · Answer

I keep getting (-1)^1 + (-1)^2 + (-1)^3 + (-1)^5 + (-1)^7 ... up til the 61st prime which is not equal to -1.

After (-1)^1 + (-1)^2 , you are left with the summation of -1's up to the 61st prime, what am I missing in this one  MartyMurray ?

Krunaal · Answer

Up till the 60th prime - so it would look like =>  (-1)^1 + (-1)^2 + (-1)^3 + (-1)^4 + (-1)^5 + (-1)^6 + (-1)^7 ............ + (-1)^{280} + (-1)^{281} , since 281 is the 60th prime.

We're not told that any integer n has to be a prime, it can be any integer up till the 60th prime => from integer 1 to the 60th prime.

gmatnoob24 · Answer

This makes sense now Krunaal, thank you! The key is if n is   ANY INTEGER UP TIL THE 60TH PRIME.   Which includes all even and odd integers. This indeed would make the answer -1. Appreciate your response.

Adidas1424 · Answer

How do we find what the 60th prime number is? Is there a particular formula we can use or do we write down all prime numbers during the exam?

Bunuel · Answer

The actual value of the 60th prime doesn’t matter, and the GMAT doesn’t expect you to know it. What matters is that it’s definitely  odd  (since 2 is the only even prime), so the sequence ends with an odd exponent. That means you’re summing (-1)^1 + (-1)^2 + ... + (-1)^odd, which always ends with -1, giving a total sum of -1, regardless of the specific value of the 60th prime.

CareerLauncherMBA · Answer

Lets find out sum of the terms from 1 to 3rd prime number (which is 5)
hence n = 1, 2, 3, 4, 5
substituting values of n to find the sum
sum = -1 + 1 - 1 + 1 - 1 = -1

Lets now take sum of the terms from 1 to 4th prime number (which is 7)
hence n = 1, 2, 3, 4, 5, 6, 7
substituting values of n to find the sum
sum = -1 + 1 - 1 + 1 - 1 + 1 - 1 = -1

Therefore, we can conclude whatever be the value of the prime number involved, the sum of the terms is -1

IMO B

Free GMAT diagnostic test from Career Launcher:
https://linkly.link/2Alsw

MartyMurray

If \(a_n = (-1)^n\), what is the sum of all \(a_n\) if \(n\) is any integer from \(1\) to the \(60\)th prime number?

(A) -2

(B) -1

(C) 0

(D) 1

(E) 2

joycechg · Answer

what if n is 2? Wouldn't that still fit the criteria and answer = 0?

Krunaal · Answer

n is any integer from 1 to 60th prime, and we want  sum of all such   a_n  's

i.e.  a_1 + a_2 + a_3 + a_4 + ................... + a_{60th-prime-no.}

joycechg · Answer

Thanks! I was thinking if the prime integer = 2, then a1+a2 = (-1)^1+(-1)^2 = -1 + 1 = 0. Am I misinterpreting?

Krunaal

Krunaal · Answer

Yes,  n = 2  is  one possible value  where  a_2 = 1 . We have to take  all the possible values  from 1 to the 60th prime, and then find its sum.

AkshayMetha · Answer

Yeah exactly.. seems some language issue with the question

If an = -1n, what is the sum of all possible values of an if n is any

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

If an = -1n, what is the sum of all possible values of an if n is any

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