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

Question

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

aa008 · Answer

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

A is the answer.

CounterSniper · Answer

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 
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

akbgmatter · Answer

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?

DavidTutorexamPAL · Answer

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.

(A) is our answer

rsrighosh · Answer

Bunuel

Could you please help with the approach 
Can this be considered as AP --> a n =a n−2 +12

Bunuel · Answer

The sequence  might  be an arithmetic progression but it's not  necessarily  an arithmetic progression.

Given  a_n=a_{n-2}+12 :

The   odd   numbered terms are:  a_3=a_{1}+12 ,  a_5=a_{3}+12 ,  a_7=a_{5}+12 , ... As you can see, the odd numbered terms are in arithmetic progression.

The   even   numbered terms are:  a_4=a_{2}+12 ,  a_6=a_{4}+12 ,  a_8=a_{6}+12 , ... As you can see, the even numbered terms are in arithmetic progression.

The sequence could be say:   1 ,  -1 ,  13 ,  11 ,  25 ,  23 ,  37 , ...  and in this case the sequence is not in arithmetic progression.

But if the sequence is say:   1 ,  7 ,  13 ,  19 ,  25 ,  31 ,  37 , ...  then the sequence will be in arithmetic progression.

The firs statement gives the value of  a_1 , an odd numbered term. We can get the values of all odd numbered terms ( a_3, \ a_5, \ a_7, \ ... ) and it turns out that 417 IS one of the odd numbered term:  a_{33}=417 . So, (1) is sufficient to give an YES answer to the question.

The second statement gives the value of  a_2 , an even numbered term. We can get the values of all even numbered terms( a_4, \ a_6, \ a_8, \ ... ) and it turns out that 417 is NOT one of the even numbered terms. But 417  could  be one of the odd numbered term, we don't know that. Thus, (2) is NOT sufficient.

The answer is A.

Hope it's clear.

TheUnenlightened · Answer

I am able to solve some 700+ questions, but here I am even having trouble understanding the provided explanations.

What's a0 then? How do we understand the road of the sequence?

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

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