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# The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in

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The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in [#permalink]  30 Jul 2018, 10:09
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Question Stats:

100% (00:13) correct 0% (00:00) wrong based on 4 sessions
The sequence P is defined by $$P_n = 10(P_{n - 1}) - 2$$ for each integer n ≥ 2. If $$P_1 = 2$$, what is the value of $$P_4$$?

[Reveal] Spoiler: OA
1778

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Sandy
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Intern
Joined: 10 Aug 2018
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Re: The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in [#permalink]  11 Aug 2018, 12:43
Simple question, just write out what P2, P3, and P4 equals using the formula. For some of these recursive sequences with a base case it helps to keep it in the original form, but when you're just asked to find P4, the number in the sequence is small enough that you don't need to complicate it by looking for patterns.

P1 = 2

P2 = 10(2) - 2 = 18

P3 = 10(18) - 2 = 180 - 2 = 178

P4 = 10(178) - 2 = 1780 - 2 = 1778
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1731 [0], given: 397

Re: The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in [#permalink]  12 Aug 2018, 04:37
Expert's post
Explanation

The sequence $$P_n = 10(P_{n – 1}) – 2$$ can be read as “to get any term in sequence P, multiply the previous term by 10 and subtract 2.”

The problem gives the first term and asks for the fourth:

 2 $$P_1$$ $$P_2$$ $$P_3$$ $$P_4$$

To get P2 , multiply 2 × 10, then subtract 2 to get 18. Continue this procedure to find each subsequent term (“to get any term in sequence P, multiply the previous term by 10 and subtract 2”). Therefore, P3 = 10(18) – 2 = 178. P4 = 10(178) – 2 = 1,778.

 2 18 178 1778 $$P_1$$ $$P_2$$ $$P_3$$ $$P_4$$

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Re: The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in   [#permalink] 12 Aug 2018, 04:37
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