The first two terms of a sequence are -3 and 2 Subsequent odd-numbered

Question

The first two terms of a sequence are -3 and 2. Subsequent odd-numbered terms are given by adding 1 to the previous term, and subsequent even-numbered terms are given by multiplying the previous term by -1. What is the sum of the first 147 terms?

A. -3
B. -2
C. -1
D. 1
E. 2

Something about this question gives me a hard time. It's a mid 600 level question but I'm struggling to wrap my head around the concept. I get that there's a pattern for this sequence, but struggling on figuring out how to apply that to the 147 terms (i think it's that 1st term at the beginning that's throwing me off).

Please help. Thanks in advance!

Please help. Thanks in advance!

niks18 · Answer

HI  henrymba2021

kindly follow the Rules of Posting. Search for the question. there is a high probability, the question would have been discussed in the relevant forum.

henrymba2021 · Answer

Hi niks18, I can't find this question in the forum. If you can point me in the right direction that would be much appreciated!

Bunuel · Answer

Please read carefully and follow our  RULES OF POSTING . Pay attention to rule 3. Thank you.

pushpitkc · Answer

Hey  henrymba2021

It has been given that the first and second terms of the sequence are -3 and 2

Third term(odd term) can be got by adding 1 to the previous term, which is 2+1 = 3
Fourth term(even) can be got by multiplying -1 to the previous term, which is -3

Fifth term = -2, Sixth term = 2, Seventh term is 3, Eight term is -3

If you observe there is a pattern where the odd and even terms cancel each other.
The 147th term will be 3.

The sum of the 147 terms will be -3 + 2 + 0 + 0 + .... + 3 =  2(Option E)

luffy_ueki · Answer

Given: The first two terms of a sequence are -3 and 2. Subsequent odd-numbered terms are given by adding 1 to the previous term, and subsequent even-numbered terms are given by multiplying the previous term by -1

Try constructing the series by following the problem stmt:
Inital terms: -3 & 2

1st term: 2+1=3, 
2nd term: 3*(-1)=-3, 
3rd term: -3+1=-2, 
4th term: -2*(-1)=2, 
5th term: 2+1=3
6th term: 3*(-1) =-3

For now, lets remove -3 & 2 the intial terms out of the sequence
By now you will notice that it follows a unique sequence: 3,-3,2,-2,3,-3 ....

odd + even terms =0
Since there are 147 -2 =145 terms there will be one term which is left out = 3

As every 4n+1 th term =3 (4n+2 th term =-3, 4n+3 th term =2, 4n+4 th term=-2)

Bring back the intial terms -3 & 2.
Thus, sum = -3 + 2 +3 =2

dave13 · Answer

Hi pushpitkc . hope you are having fantastic GMAT weekend with GMATclub

now back to question:-) why the first two letters and the last 3 didnt cancel out if other numbers canceled out ?

-3 + 2 + 0 + 0 + .... + 3 thanks!

pushpitkc · Answer

Hi  dave13

First term is -3
Second term is 2
Third(3) and fourth term(-3) cancel each other out.
Seventh(-2) and eighth term(2) cancel each other out.
Ninth(3) and tenth term(-3) cancel each other out.
.
.
We observe a pattern in the terms from 3rd term(3 -3 -2 2 3 -3 -2 2 3 -3 -2 2.....)
.
.
145th term(-2) and 146th term(2) cancel each other out.
147th term will be 3.

So sum is -3 + 2 + 3+ (-3) + (-2) + 2 ......... + (-2) + 2 + 3 = -3 + 2 + 3 = 2

P.S The alternate terms starting from the 3rd term till the 146th term cancel each other out

Hope this helps clear your confusion.

aviddd · Answer

Enjoyed solving this question, though it took me >3 mins to figure out.

MathRevolution · Answer

First term: -3   ;   Second term: 2

=> Third term: 2 + 1 = 3

=> Fourth term: 3 * (-1) = - 3

=> Fifth term:   = - 3 + 1 = -2

=> Sixth term: -2 * (-1) =   =   2    .

=> Seventh term = Third term.

Pattern:  -3 ,   , 3, -3, -2],   , 3, -3, -2]

Sum of 4 numbers in 1 pair: 2 + 3 - 3 - 2 = 0.

We can form 36 pairs   giving sum = 0.

First number (-3) + 144 numbers (sum = 0) = Total 145 numbers.
 
Left out numbers are:  1^{st}  = -3,  146^{th}  = 2 ,  147^{th}  = 3

Sum: -3 + 2 + 3 = 2

Answer E

Adit_ · Answer

The sequence after a1 and a2 is like:

3,-3,-2,2,3,-3...

Every four terms the values repeat again, each time giving a sum of 0.

Thus taking the first two terms away we have 145 terms.

145 mod 4 = 1
So 1 extra term will be the 1st term of our sequence of 3,-3,-2,2 = 3

First two terms sum = a1+a2 = -3+2 = -1
Thus net sum = 3+(-1) = 2.

Answer:  Option E

The first two terms of a sequence are -3 and 2 Subsequent odd-numbered

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The first two terms of a sequence are -3 and 2 Subsequent odd-numbered

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