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

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1650 [0], given: 396

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

66% (00:22) correct 33% (01:14) wrong based on 6 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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Sandy
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Director
Joined: 07 Jan 2018
Posts: 550
Followers: 4

Kudos [?]: 476 [0], given: 84

Re: In sequence Q, the first number is 3, and each subsequent nu [#permalink]  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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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [0], given: 396

Re: In sequence Q, the first number is 3, and each subsequent nu [#permalink]  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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Sandy
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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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