Each of the even-numbered terms in a certain sequenceis formed by multiplying the preceding term...

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AAPL: Moderator; Posts: 2672; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue Nov 24, 2020 5:28 pm

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Princeton Review

Each of the even-numbered terms in a certain sequence is formed by multiplying the preceding term by –1. Each of the odd-numbered terms in the sequence is formed by adding 3 to the preceding term. If the first term in the sequence is 3, then what is the 168th term?

A. -3
B. -1
C. 0
D. 1
E. 3

OA C

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: Each of the even-numbered terms in a certain sequenceis formed by multiplying the preceding term...

by deloitte247 » Fri Nov 27, 2020 4:57 am

- Even terms are formed by multiplying the preceding term by - 1
- Odd terms are formed by adding 3 to the preceding term by 3
- First term = 3
1st term = 3
2nd term = 3 * (-1) = -3
3rd term = -3 + 3 = 0
4th term = 0 * -1 = 0
5th term = 0 + 3 = 3
6th term = 3 * - 1 = -3
7th term = - 3 + 3 = 0
8th term = 0 * -1 = 0
Every third and fourth term in the series yields 0
Since 168/4 = 42 168th term will be one of the fifth term and will be 0

Answer = C

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Re: Each of the even-numbered terms in a certain sequenceis formed by multiplying the preceding term...

by Scott@TargetTestPrep » Mon Nov 30, 2020 10:42 am

AAPL wrote: ↑
Tue Nov 24, 2020 5:28 pm
Princeton Review

Each of the even-numbered terms in a certain sequence is formed by multiplying the preceding term by –1. Each of the odd-numbered terms in the sequence is formed by adding 3 to the preceding term. If the first term in the sequence is 3, then what is the 168th term?

A. -3
B. -1
C. 0
D. 1
E. 3

OA C

Solution:

Let a_n be the nth term. We see that:

a_1 = 3
a_2 = -3
a_3 = 0
a_4 = 0
a_5 = 3,
a_6 = -3
a_7 = 0
a_8 = 0

We see that the terms repeat in a four-number pattern: 3, -3, 0, 0. Note that the 4th, 8th, and 12th terms are equal to 0, and any term number that is a multiple of 4 is also equal to 0. Since 168 is a multiple of 4, the 168th term is also equal to 0..

Answer: C

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