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In sequence Q, the first number is 3, and each subsequent nu

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GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1783 [0], given: 397

In sequence Q, the first number is 3, and each subsequent nu [#permalink] New post 30 Jul 2018, 10:16
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Question Stats:

62% (00:31) correct 37% (01:50) wrong based on 8 sessions
In sequence Q, the first number is 3, and each subsequent number in the sequence is determined by doubling the previous number and then adding 2. In the first 10 terms of the sequence, how many times does the digit 8 appear in the units digit?

[Reveal] Spoiler: OA
9

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Joined: 07 Jan 2018
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Kudos [?]: 546 [0], given: 88

Re: In sequence Q, the first number is 3, and each subsequent nu [#permalink] New post 31 Jul 2018, 06:59
From the question stem:
The first term is 3
The second term is 3*2 + 2 = 8
The third term is 8*2 + 2 = 18

We can see that when the unit digit 8 is multiplied by 2 it ends with 6 and when 2 is added it becomes 8 hence all the terms except the first have their units digit as 8. In total there are 9 such terms
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GRE Prep Club Legend
GRE Prep Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: In sequence Q, the first number is 3, and each subsequent nu [#permalink] New post 12 Aug 2018, 07:04
Expert's post
Explanation

After the first term in the sequence, every term has a units digit of 8:

\(Q_1 = 3\)
\(Q_2 = 2(3) + 2 = 8\)
\(Q_3 = 2(8) + 2 = 18\)
\(Q_4 = 2(18) + 2 = 38\)
\(Q_5 = 2(38) + 2 = 78\)
…

So 8 is the units digit nine out of the first ten times.
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Re: In sequence Q, the first number is 3, and each subsequent nu   [#permalink] 12 Aug 2018, 07:04
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In sequence Q, the first number is 3, and each subsequent nu

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