A sequence is defined by $s_n=(s_{n-1}-1)(s_{n-2})$ for $n > 2,$ and it has the starting values of $s_1=2$ and

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Jul 22, 2020 12:50 pm

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A sequence is defined by $s_n=(s_{n-1}-1)(s_{n-2})$ for $n > 2,$ and it has the starting values of $s_1=2$ and $s_2=3.$ Find the value of $s_6.$

A. 25
B. 32
C. 36
D. 93
E. 279

[spoiler]OA=E[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Wed Jul 22, 2020 12:50 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

Re: A sequence is defined by $s_n=(s_{n-1}-1)(s_{n-2})$ for $n > 2,$ and it has the starting values of $s_1=2$ and

by Jay@ManhattanReview » Wed Jul 22, 2020 10:56 pm

Vincen wrote: ↑
Wed Jul 22, 2020 12:50 pm
A sequence is defined by $s_n=(s_{n-1}-1)(s_{n-2})$ for $n > 2,$ and it has the starting values of $s_1=2$ and $s_2=3.$ Find the value of $s_6.$

A. 25
B. 32
C. 36
D. 93
E. 279

[spoiler]OA=E[/spoiler]

Source: Magoosh

Pluggin-in the value of n = 3 in $s_n=(s_{n-1}-1)(s_{n-2}),$ we get $s_3=(s_2-1)(s_1)$.

Again, $s_3=(s_2-1)(s_1) = (3-1)*2=4$

Similarly, $s_4=(s_3-1)(s_2) = (4-1)*3=9$

And, $s_5=(s_4-1)(s_3) = (9-1)*4=32$

And finally, $s_6=(s_5-1)(s_4) = (32-1)*9=279$

Correct answer: E

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A sequence is defined by $s_n=(s_{n-1}-1)(s_{n-2})$ for $n > 2,$ and it has the starting values of $s_1=2$ and

by Scott@TargetTestPrep » Sat Jul 25, 2020 2:14 pm

Vincen wrote: ↑
Wed Jul 22, 2020 12:50 pm
A sequence is defined by $s_n=(s_{n-1}-1)(s_{n-2})$ for $n > 2,$ and it has the starting values of $s_1=2$ and $s_2=3.$ Find the value of $s_6.$

A. 25
B. 32
C. 36
D. 93
E. 279

[spoiler]OA=E[/spoiler]

Solution:

s(3) = (s(2) - 1)(s(1)) = (3 - 1)(2) = 4

s(4) = (s(3) - 1)(s(2)) = (4 - 1)(3) = 9

s(5) = (s(4) - 1)(s(3)) = (9 - 1)(4) = 32

s(6) = (s(5) - 1)(s(4)) = (32 - 1)(9) = 279

Answer: E

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