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# In a certain sequence, term a_n can be found using the formula

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Intern
Joined: 04 Feb 2018
Posts: 10
Location: India
In a certain sequence, term a_n can be found using the formula  [#permalink]

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Updated on: 06 Oct 2018, 03:04
1
3
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Difficulty:

95% (hard)

Question Stats:

32% (01:23) correct 68% (02:05) wrong based on 60 sessions

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In a certain sequence, term $$a_n$$ can be found using the formula $$a_n=a_{n-2}+12$$, where n >= 2. Is 417 a term of this sequence?

(1) $$a_1 = 21$$
(2) $$a_2 = 23$$

Originally posted by rheabiswal on 01 Oct 2018, 23:41.
Last edited by Bunuel on 06 Oct 2018, 03:04, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 05 Oct 2017
Posts: 20
Re: In a certain sequence, term a_n can be found using the formula  [#permalink]

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02 Oct 2018, 01:16
1
1
rheabiswal wrote:
In a certain sequence,
term $$a_n$$ can be found using the formula $$a_n$$=$$a_{n-2}$$+12, where n>=2. is 417 a term of this sequence?

1.$$a_1$$ = 21
2. $$a_2$$ = 23

Using statement 1: A1= 21 so A3= 33, A4=45

So all the odd term will be 21+12n (where n=0,1,2,3....)
and 417=21+33*12

417 is 33th term of series.

A is sufficient to answer question

Using statement 2:

all the even term will 23+12n (where n=0,1,2,3....)
417 is not a even term of the series , it may be odd term.

B is not sufficient to answer question

Director
Joined: 20 Feb 2015
Posts: 793
Concentration: Strategy, General Management
Re: In a certain sequence, term a_n can be found using the formula  [#permalink]

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02 Oct 2018, 01:36
1
rheabiswal wrote:
In a certain sequence,
term $$a_n$$ can be found using the formula $$a_n$$=$$a_{n-2}$$+12, where n>=2. is 417 a term of this sequence?

1.$$a_1$$ = 21
2. $$a_2$$ = 23

1.$$a_1$$ = 21

a_3 = 21+12 = 33
a_4 = 33+12 = 45
...
we get an AP with 1st term as 21 and common difference as 12
assume 417 to be nth term in this series
therefore
417 = 21+(n-1)d
417 = 21+(n-1)12
417 = 9+12n
n=408/12
n=34 (evenly divides 408)
sufficient

2. $$a_2$$ = 23[/quote]
same as above
we have an AP
with common difference as 12 and first term as 23
so,
417=23+(n-1)12
417=11+12n
n=406/12
12 does not evenly divides 406 , now what we know from here is that the value is not a part of even terms such as $$a_34$$,$$a_36$$,$$a_38$$ , but we are not sure of the odd terms such as $$a_33$$ or $$a_35$$ or $$a_37$$
therefore
not sufficient

A
Intern
Joined: 10 Sep 2018
Posts: 3
Re: In a certain sequence, term a_n can be found using the formula  [#permalink]

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05 Oct 2018, 23:12
In a certain sequence, term an can be found using the formula $$a_n$$=$$a_{n-2}$$+12, where n≥2 is an integer. Is 417 a term of this sequence?

1) $$a_1$$=21

2) $$a_2$$=23

Is there a quick way to answer such type of questions?
examPAL Representative
Joined: 07 Dec 2017
Posts: 721
Re: In a certain sequence, term a_n can be found using the formula  [#permalink]

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05 Oct 2018, 23:18
1
akbgmatter wrote:
In a certain sequence, term an can be found using the formula $$a_n$$=$$a_{n-2}$$+12, where n≥2 is an integer. Is 417 a term of this sequence?

1) $$a_1$$=21

2) $$a_2$$=23

Is there a quick way to answer such type of questions?

Hey akbgmatter,
Yes, there is!

Since the formula gives us the connection between $$a_{n-2}$$ and $$a_n$$, once you know the value of 1 even member of the sequence, you can calculate the value of ANY even number of the sequence. Simlarly, one odd element gives you all the odd elements. So, to know the value of the 417th element you need to know the value of some other odd element of the sequence
We'll look for an answer that gives us this information, a Logical approach.

(1) exactly what we need!
Sufficient.

(2) no information on the odd elements of the sequence...
Insufficient.

_________________

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Intern
Joined: 10 Sep 2018
Posts: 3
Re: In a certain sequence, term a_n can be found using the formula  [#permalink]

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05 Oct 2018, 23:37
Quote:
So, to know the value of the 417th element you need to know the value of some other odd element of the sequence
We'll look for an answer that gives us this information, a Logical approach.

(1) exactly what we need!
Sufficient.

(2) no information on the odd elements of the sequence...
Insufficient.

Hey DavidTutorexamPAL!
Thanks for your quick response, the question asks if 417 is a term of the sequence of which two elements are given in problem choices. I later found an approach mentioned in below link (which didn't show up in the first search while looking for this problem on the forum)
"/forum/in-a-certain-sequence-term-a-n-can-be-found-277790.html?fl=similar"

Cheers!!
Re: In a certain sequence, term a_n can be found using the formula &nbs [#permalink] 05 Oct 2018, 23:37
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