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In a sequence of positive integers, every odd-numbered term after the

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In a sequence of positive integers, every odd-numbered term after the  [#permalink]

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New post 08 Mar 2019, 00:06
2
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (02:40) correct 30% (02:41) wrong based on 44 sessions

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In a sequence of positive integers, every odd-numbered term after the first term is 1 more than twice the previous term and every even-numbered term starting from the 2nd term, is 2 less than 3 times the previous term. If the 2nd term of the sequence is 1, then how many terms out of the first 20 terms are even?

A. 0
B. 5
C. 10
D. 15
E. 20
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Re: In a sequence of positive integers, every odd-numbered term after the  [#permalink]

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New post 08 Mar 2019, 02:00
1

Solution


Given:
    • In a sequence of positive integers, every odd-numbered term after the first term is 1 more than twice the previous term and every even-numbered term starting from the 2nd term, is 2 less than 3 times the previous term.
    • The 2nd term of the sequence is 1.

To find:
    • Number of even terms in the first 20 terms of the series.

Approach and Working:
The 2nd term is 1 and it is 2 less than 3 times the 1st term
    • Therefore, the 1st term = (1 + 2)/3 = 1
So, both 1st and 2nd terms are odd numbers.

For odd numbered terms,
    • Value = 2 x previous term + 1 = even + odd = odd

For even numbered terms,
    • Value = 3 x previous term – 2 = 3 x odd – 2 = odd – even = odd

Therefore, all the terms in the series is odd.

Hence, the correct answer is option A.

Answer: A

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Re: In a sequence of positive integers, every odd-numbered term after the  [#permalink]

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New post 08 Mar 2019, 04:59
Look for odd & even numbers in the sequence. All numbers turn out to be odd. Hence even numbers are 0.
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Re: In a sequence of positive integers, every odd-numbered term after the  [#permalink]

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New post 10 Mar 2019, 09:56
kiran120680 wrote:
In a sequence of positive integers, every odd-numbered term after the first term is 1 more than twice the previous term and every even-numbered term starting from the 2nd term, is 2 less than 3 times the previous term. If the 2nd term of the sequence is 1, then how many terms out of the first 20 terms are even?

A. 0
B. 5
C. 10
D. 15
E. 20


first term =
1 more than twice the previous term = 1 + 2* previous term
even term + odd (1) = odd term always
2nd term
2 less than 3 times the previous term
previous term odd ie odd 3*odd -2 = odd-2 = odd term
so even terms = 0
IMO A
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Re: In a sequence of positive integers, every odd-numbered term after the   [#permalink] 10 Mar 2019, 09:56
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