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A certain series of numbers has 15 terms in total. The first term of

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A certain series of numbers has 15 terms in total. The first term of  [#permalink]

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New post 15 May 2019, 02:01
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

43% (02:24) correct 57% (02:19) wrong based on 74 sessions

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A certain series of numbers has 15 terms in total. The first term of the sequence is -4. From the second term, every even numbered term is 3 more than the previous term, and every odd numbered term is 2 less than the previous term. How many terms are positive in the given series?

    A. 7
    B. 8
    C. 9
    D. 10
    E. 11


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Re: A certain series of numbers has 15 terms in total. The first term of  [#permalink]

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New post 15 May 2019, 10:12
Based on my understanding of the question ; solution as follows;

a1=-4
a2=-4+3;-1
a3=-1-2;-3
continue with same logic until a15
a4;0
a5;-2
a6;1
a7;-1
a8;2
a9;0
a10;3
a11;1
a12;4
a13;2
a14;5
a15;3

not to count 0 ; we get get 8 +ve integers
IMO B


EgmatQuantExpert wrote:
A certain series of numbers has 15 terms in total. The first term of the sequence is -4. From the second term, every even numbered term is 3 more than the previous term, and every odd numbered term is 2 less than the previous term. How many terms are positive in the given series?

    A. 7
    B. 8
    C. 9
    D. 10
    E. 11


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Posts: 3142
Re: A certain series of numbers has 15 terms in total. The first term of  [#permalink]

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New post 20 May 2019, 04:03

Solution


Given:
In this question, we are given that
    • A certain series of numbers has 15 terms in total.
    • The first term of the sequence is -4.
    • From the second term, every even numbered term is 3 more than the previous term, and every odd numbered term is 2 less than the previous term.

To find:
We need to determine
    • The number of terms in the series, which are positive.

Approach and Working:
Let us determine the values of the individual terms, using the value of the first term.
    • Term 1 = -4
    • Term 2 = -4 + 3 = -1
    • Term 3 = -1 – 2 = -3
    • Term 4 = -3 + 3 = 0
    • Term 5 = 0 – 2 = -2
    • Term 6 = -2 + 3 = 1
    • Term 7 = 1 – 2 = -1
    • Term 8 = -1 + 3 = 2
    • Term 9 = 2 – 2 = 0
    • Term 10 = 0 + 3 = 3

Term 10 onwards all the terms will be positive.

As we can see, there are total 7 terms present in the series, which are either negative or 0.
    • Therefore, the number of positive terms = 15 – 7 = 8

Hence, the correct answer is option B.

Answer: B

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Re: A certain series of numbers has 15 terms in total. The first term of   [#permalink] 20 May 2019, 04:03
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