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If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a

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Director
Joined: 07 Aug 2011
Posts: 538
GMAT 1: 630 Q49 V27
If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a  [#permalink]

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Updated on: 09 Apr 2015, 05:26
3
00:00

Difficulty:

35% (medium)

Question Stats:

78% (02:30) correct 22% (02:35) wrong based on 92 sessions

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If the a-th term of a certain sequence is given by $$(-1)^a + (-0.1)^a,$$ then the sum of the terms from 1 to 5 is

A. -1.11111
B. -1.09091
C. 0
D. 0.90909
E. 1.11111

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Originally posted by Lucky2783 on 09 Apr 2015, 05:00.
Last edited by Bunuel on 09 Apr 2015, 05:26, edited 1 time in total.
Edited the question.
Director
Joined: 07 Aug 2011
Posts: 538
GMAT 1: 630 Q49 V27
Re: If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a  [#permalink]

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09 Apr 2015, 05:24
Lucky2783 wrote:
If the a-th term of a certain sequence is given by $$(-1)^a + (-0.1)^a,$$ then the sum of the terms from 1 to 5 is
A. -1.11111
B. -1.09091
C. 0
D. 0.90909
E. 1.11111

One of the possible solutions :

the resultant series is

$$(-1)^1+(-1)^2+(-1)^3+(-1)^4+(-1)^5 =\frac{(-1) (1-(-1)^5)}{(1-(-1))}$$ = -1

$$(-0.1)^1+(-0.1)^2+(-0.1)^3+(-0.1)^4+(-0.1)^5 =\frac{(-0.1) (1-(-0.1)^5)}{(1-(-0.1))}$$ = -0.09091

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Lucky

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Intern
Joined: 26 Aug 2014
Posts: 46
GMAT 1: 650 Q49 V30
GMAT 2: 650 Q49 V31
WE: Programming (Computer Software)
Re: If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a  [#permalink]

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09 Apr 2015, 10:39
When a is 1,3 or 5, we will get a negative number and when it is 2 or 4 we will get a positive number.
Considering the above, we will be left with -1 + (-0.1)^a
So answer choices C, D, and E are eliminated.

Also notice, we will get answer choice A when all results of (-0.1)^a are negative, which is not the case.

So the correct answer is B.

Alternately, you can add the following:

-1 -0.1+0.01-0.001+0.0001-0.00001 = -1.09091

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Re: If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a  [#permalink]

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29 Jul 2018, 21:56
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Re: If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a &nbs [#permalink] 29 Jul 2018, 21:56
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