rsrighosh wrote:
BunuelCould you please help with the approach
Can this be considered as AP --> a
n=a
n−2+12
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.
_________________