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The sequence a1, a2, a3, . . . , an, . . . is such that an = 3an−1 + 2

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V
Joined: 02 Sep 2009
Posts: 58431
The sequence a1, a2, a3, . . . , an, . . . is such that an = 3an−1 + 2  [#permalink]

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New post 21 Jan 2019, 03:27
1
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

95% (01:51) correct 5% (00:54) wrong based on 26 sessions

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Location: India
Re: The sequence a1, a2, a3, . . . , an, . . . is such that an = 3an−1 + 2  [#permalink]

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New post 21 Jan 2019, 06:42
Bunuel wrote:
The sequence \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ... is such that \(a_n = 3a_{n−1} + 2a_{n−2}\) for all \(n > 2\). If \(a_3 = 7\) and \(a_4 = 35\), what is \(a_2\)?

A 7
B 14
C 17
D 19
E 21


if \(a_3 = 7\) and \(a_4 = 35\)

\(a_3 = 3 a_2 + 2 a_1\) (a)
\(a_4 = 3 a_3 + 2 a_2\) (b)

Multiply (a) by 2 and (b) by 3

\(2 a_3 = 6 a_2 + 4 a_1\)
\(3 a_4 = 9 a_3 + 6 a_2\)

Now subtract above equations to get

\(2 a_3 - 3 a_4 = - 9 a_3 + 4 a_1\)
get a relationship as \(11 a_3 = 3 a_4 + 4 a_1\)
\(a_1 = -7\)

\(a_3 = 3 a_2 + 2 a_1\)
\((a_3 - 2 a_1)/ 3 = 3 a_2\)
\(a_2 = 7\)

Answer A
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Re: The sequence a1, a2, a3, . . . , an, . . . is such that an = 3an−1 + 2  [#permalink]

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New post 21 Jan 2019, 09:13
Bunuel wrote:
The sequence \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ... is such that \(a_n = 3a_{n−1} + 2a_{n−2}\) for all \(n > 2\). If \(a_3 = 7\) and \(a_4 = 35\), what is \(a_2\)?

A 7
B 14
C 17
D 19
E 21


given expression

an=3 an-1+ 2an-2
a4= 3a3+2a2
solve
a4 & a3 given
2a2= 14
a2= 7
IMO A
GMAT Club Bot
Re: The sequence a1, a2, a3, . . . , an, . . . is such that an = 3an−1 + 2   [#permalink] 21 Jan 2019, 09:13
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