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# The nth term in a certain sequence is defined for positive integer n a

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Math Expert
Joined: 02 Sep 2009
Posts: 59182
The nth term in a certain sequence is defined for positive integer n a  [#permalink]

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22 Sep 2016, 04:41
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Difficulty:

85% (hard)

Question Stats:

59% (02:25) correct 41% (02:16) wrong based on 132 sessions

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The nth term in a certain sequence is defined for positive integer n as $$\frac{1+(-1)^{(\frac{n(n+1)}{2})}}{2}$$. What is the total of the first 64 terms of this sequence?

A. −164
B. 0
C. 16
D. 32
E. 64

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Re: The nth term in a certain sequence is defined for positive integer n a  [#permalink]

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22 Sep 2016, 05:08
1
sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term)

sum of 64 terms = 32

I go with D
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Joined: 06 Oct 2015
Posts: 86
Re: The nth term in a certain sequence is defined for positive integer n a  [#permalink]

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29 Oct 2016, 03:02
deepthit wrote:
sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term)

sum of 64 terms = 32

I go with D

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Re: The nth term in a certain sequence is defined for positive integer n a  [#permalink]

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29 Oct 2016, 07:38
3
Top Contributor
Bunuel wrote:
The nth term in a certain sequence is defined for positive integer n as $$\frac{1+(-1)^{(\frac{n(n+1)}{2})}}{2}$$. What is the total of the first 64 terms of this sequence?

A. −164
B. 0
C. 16
D. 32
E. 64

To find term1, replace n with 1 in the expression $$\frac{1+(-1)^{(\frac{n(n+1)}{2})}}{2}$$
We find that term1 = 0

To find term2, replace n with 2 in the expression $$\frac{1+(-1)^{(\frac{n(n+1)}{2})}}{2}$$
We find that term2 = 0

To find term3, replace n with 3 in the expression. We find that term3 = 1

To find term4, replace n with 4 in the expression. We find that term4 = 1

Term5 = 0

Term6 = 0

Term7 = 1

Term8 = 1
.
.
.

So, the SUM of the first 64 terms of the sequence = 0 + 0 + 1 + 1 + 0 + 0 + 1 + 1 .....

As we can see, HALF of the terms will be 0 and HALF will be 1
In other words, 32 terms will equal 0 and 32 terms will equal 1
So, the sum = (32)(0) + (32)(1) = 32

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Re: The nth term in a certain sequence is defined for positive integer n a  [#permalink]

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13 Oct 2019, 16:14
I don't know what am i doing wrong but I don't get the answers as 0,1,0,1...
The second term is -1 and my third term when I replace n with 3 is= -2.5

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Joined: 09 Oct 2019
Posts: 2
Re: The nth term in a certain sequence is defined for positive integer n a  [#permalink]

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13 Oct 2019, 18:07
-1^odd = -1
-1^even = 1

If we put (-1^odd) to formula, equal to 0
So we have to find how many n that equal to 1

Find 1/2 [n(n+1)] that equals even
Means n(n+1) = multiple of four 4
1.2 = no
2.3 = no
3.4 = yes
4.5 = yes
... so on

it is half of 64, so 1/2 * 64 = 32
Re: The nth term in a certain sequence is defined for positive integer n a   [#permalink] 13 Oct 2019, 18:07
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