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

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GMAT Club Legend
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Joined: 07 Jun 2014
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The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in [#permalink] New post 30 Jul 2018, 10:09
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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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Re: The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in [#permalink] New post 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
GMAT Club Legend
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Re: The sequence P is defined by Pn = 10(Pn – 1) – 2 for each in [#permalink] New post 12 Aug 2018, 04:37
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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.


2181781778
\(P_1\)\(P_2\)\(P_3\)\(P_4\)

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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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