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In a sequence, all the terms are arranged

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In a sequence, all the terms are arranged  [#permalink]

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New post 31 Jul 2019, 05:12
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Question Stats:

92% (01:17) correct 8% (01:07) wrong based on 51 sessions

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Algerba Question Series- Question 1



In a sequence, all the terms are arranged in decreasing order of value, and the difference between any two consecutive terms is equal to 4. If the number of terms in the sequence is odd, and the sum of first term and last term is zero, then what is the sum of all terms in the sequence?

    A. 0
    B. 4
    C. 8
    D. 12
    E. 16
Spoiler: OA

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Re: In a sequence, all the terms are arranged  [#permalink]

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New post 31 Jul 2019, 06:48
Checking all conditions of the question.
First: the number of terms is odd. For example; n=5
Second:The sum of the first and last terms is zero.
So these are negative and positive like 8 & -8

The sum of all numbers would be zero
Option A

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Re: In a sequence, all the terms are arranged  [#permalink]

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New post 31 Jul 2019, 06:50
EgmatQuantExpert wrote:

Algerba Question Series- Question 1



In a sequence, all the terms are arranged in decreasing order of value, and the difference between any two consecutive terms is equal to 4. If the number of terms in the sequence is odd, and the sum of first term and last term is zero, then what is the sum of all terms in the sequence?

    A. 0
    B. 4
    C. 8
    D. 12
    E. 16


The problem does not state anything about the number of terms in the sequence.
So, take the sequence to contain only one term.

A sequence of one term satisfies the following required conditions.
  • Difference between any two consecutive terms is equal to 4.
  • Number of terms in the sequence should be odd.

For the last condition (sum of first and last terms is zero) to be met, the one term in the sequence should be \(0\).
\(\implies\) sum of all the terms in the sequence is \(0\).

Answer is A.
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Re: In a sequence, all the terms are arranged  [#permalink]

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New post 05 Aug 2019, 21:56

Solution


Given:
    • In a sequence, all the terms are arranged in decreasing order of value
    • The difference between any two consecutive terms is equal to 4.
    • The number of terms in the sequence is odd, and
    • The sum of first term and last term is zero

To find:
    • The sum of all terms in the sequence

Approach and Working Out:
    • Let the terms in the sequence be: a, a – d, a – 2d, a – 3d, …., a + (n – 1) * d, where d = 4
    • We are given that,
      o a + a + (n – 1) * 4 = 0
      o Implies. 2a + 4(n – 1) = 0

    • Sum of all terms = \([2a + (n – 1) * 4] * \frac{n}{2} = 0 * \frac{n}{2} = 0\)

Hence, the correct answer is Option A.

Answer: A

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Re: In a sequence, all the terms are arranged   [#permalink] 05 Aug 2019, 21:56
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