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

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Joined: 02 Sep 2009
Posts: 51263
The first term of a sequence is -2 and the second term is 2. Each  [#permalink]

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21 Aug 2015, 03:59
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Difficulty:

45% (medium)

Question Stats:

70% (02:15) correct 30% (02:18) wrong based on 148 sessions

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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.

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Posts: 652
Re: The first term of a sequence is -2 and the second term is 2. Each  [#permalink]

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21 Aug 2015, 05:01
2
1
Bunuel wrote:
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.

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
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Re: The first term of a sequence is -2 and the second term is 2. Each  [#permalink]

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21 Aug 2015, 05:52
1
Bunuel wrote:
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_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.
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Re: The first term of a sequence is -2 and the second term is 2. Each  [#permalink]

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21 Aug 2015, 20:43
1
Bunuel wrote:
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

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
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Re: The first term of a sequence is -2 and the second term is 2. Each  [#permalink]

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21 Aug 2015, 21:49
1
-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
Math Expert
Joined: 02 Sep 2009
Posts: 51263
Re: The first term of a sequence is -2 and the second term is 2. Each  [#permalink]

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23 Aug 2015, 11:18
Bunuel wrote:
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.

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.
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Re: The first term of a sequence is -2 and the second term is 2. Each  [#permalink]

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29 Jul 2018, 23:04
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Re: The first term of a sequence is -2 and the second term is 2. Each &nbs [#permalink] 29 Jul 2018, 23:04
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