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Which of the following is not an arithmetic sequence?

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rishit1080
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Which of the following is not an arithmetic sequence? [#permalink] New post   27 Oct 2016, 08:18
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In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic sequence a, b, c, d, e, each term after the first is the sum of the preceding term and the constant k. Which of the following is NOT an arithmetic sequence?


A. a, b − 1, c − 2, d − 3, e − 4

B. a – 1, b – 1, c – 1, d – 1, e − 1

C. a − 1, b – 2, c – 3, d − 4, e − 5

D. a, 2b, 3c, 4d, 5e

E. 3a, 3b, 3c, 3d, 3e
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Re: Which of the following is not an arithmetic sequence? [#permalink] New post   27 Oct 2016, 10:11
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rishit1080 wrote:
In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic sequence a, b, c, d, e, each term after the first is the sum of the preceding term and the constant k. Which of the following is NOT an arithmetic sequence?


A. a, b − 1, c − 2, d − 3, e − 4

B. a – 1, b – 1, c – 1, d – 1, e − 1

C. a − 1, b – 2, c – 3, d − 4, e − 5

D. a, 2b, 3c, 4d, 5e

E. 3a, 3b, 3c, 3d, 3e


Similar question to practice: an-arithmetic-sequence-is-a-sequence-in-which-each-term-59035.html
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Re: Which of the following is not an arithmetic sequence? [#permalink] New post   06 Sep 2017, 08:05
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rishit1080 wrote:
In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic sequence a, b, c, d, e, each term after the first is the sum of the preceding term and the constant k. Which of the following is NOT an arithmetic sequence?


A. a, b − 1, c − 2, d − 3, e − 4

B. a – 1, b – 1, c – 1, d – 1, e − 1

C. a − 1, b – 2, c – 3, d − 4, e − 5

D. a, 2b, 3c, 4d, 5e

E. 3a, 3b, 3c, 3d, 3e


We have arithmetic sequence:
a
b = a+k
c = a+2k
d = a+3k
e = a+4k

Checking options.
A.
b-1 = a+k-1
c-2 = a+2k-2
d-3 = a+3k-3
e-4 - a+4k-4
So the constat here is k-1. Yes, it is arithmetic sequence.
And so on.
Option D fits.

But this approach takes 2 much time.
It will be faster if we just check on numbers. a = 1, b = 2, c = 3, d = 4, e = 5.
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Re: Which of the following is not an arithmetic sequence? [#permalink] New post   25 May 2020, 15:34
D

Consider a= a; b =a+1; c = a + 2; d = a + 3; e =a +4.

Putting values of a,b,c,d,e for all options, only D does not form AM sequence
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Re: Which of the following is not an arithmetic sequence? [#permalink]
25 May 2020, 15:34
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