A sequence, a1=64, a2=66, a3=67, an=8+an-3, which of the

Question

A sequence, a1=64, a2=66, a3=67, an=8+an-3, which of the following is in the sequence?

105 
786 
966 
1025 
I tried plugging in nos and got the right answer, but that was very time consuming. Is there any shortcut?

aaron22197 · Answer

The terms are not in a sequence--> 64,66,67 and I do not understand a(N). Is there a typo in your question?

rpmodi · Answer

Is the answer 786 ?

I expanded the sequence just a bit further

so sequence will be 64 , 66, 67 , 72 , 74 , 75 ,..........

if you look at the property of any number in this sequence , number has to be divisible by 8 or have reminder of 2 or reminder of 3.....

divide all the numbers in answer choice; only 786 gives us remainder of 2 , other options are giving remainder of 1 or 6 and so can't be part of this sequence .

This is the best approach I could think of , it would be interesting to see even faster approach .

FN · Answer

tough question but i realized that the numbers have to be within +3 of a multiple of 8..

8N+3=..

basically 1025 is the only that fits the bill..

8n=1025-3..is it a multiple of 8 YES

Can I ask where you got this question from??

FN · Answer

look at it from my view point

a-2=56, a-1=58 a0=59, a1=64, a2=66, a3=67..a4=72 a5=74, a6=75, a7=80..

every 3 points you have a multiple of 8..

so i deduced that 8N+3=number in the sequence..

what do you think??

rpmodi · Answer

I don't quiet follow that approach

1st reason even if we assume 8N+3 is the correct generalization 1025 is not 8N+3 its rather 8N+1

2nd reason there are three patterns which repeat so we can't deduce the single equation

I rather put the sequence the following way

8N , 8N+2 , 8N+3 , so on and so forth ....

so any number in the answer choice meeting one of these requirements will be the correct answer .

ritula · Answer

Guess wht? i also followed the same approach. Yup B is the right answer, but i m looking for a short cut.I found this time consuming.

rpmodi · Answer

If someone can come up with faster approach as in how to generalize the sequence ,that definitely will be helpful .But I feel in these kind of question in which " which of this fits the solution " is asked we really have to look at each choice , unlike in which simple algebra, geometry formula etc. will yield to a single answer

FN · Answer

yeah, you are right..i messed up on 1025..it is indeed 8n-1..

basically the pattern as you mentioned is the remainder of 2 or 3..or for that matter 0..

so agree with B

aaron22197 · Answer

one strategy to answer it faster would be to look at odd and even combination of the numbers.

8N is even
8N+2 is even
8N +3 is odd

so, odd answer choices must be 8N+3
even answer choices must be the other two.

I am not sure how much this helps. But it is a strategy.

A sequence, a1=64, a2=66, a3=67, an=8+an-3, which of the

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