Hi Manish Sen,

In the question, it is only mentioned that the sequence given is a non-decreasing one. Therefore we can't use the formula for the sum of 'n' of an A.P.

I hope this helps.

Hi Snehal Soman,
This is CAT 2022 question.

Hi, your approach is wrong. No where is it given that you need three values for a sequence, a sequence can be a single value as well. Considering that, you will get the correct answer.
Hope this helps!

How can a single value be a sequence? And even if it is not given in the question isn't it common sense that at least 3 values are required to establish a sequence like an universal truth kind of a scenario?

Hi, in this case it cannot because 20N is not equal to 300N, In this question, it is implied that we are dealing with a sequence of N numbers, which means $$N\ge1$$. A sequence, technically speaking, can consist of just one number, if it would still satisfy the condition of being non-decreasing and satisfy the other side of the equation. We are tasked to find the different values that satisfies N. If in a scenario where a single value satisfied the 300N condition, that would be valid value. Please don't hold on to any premonitions about "universal truths". Just stick to what the question is asking.

Hi,
Can you please let me know the source of this question ? (eg CAT 2020 or XAT 2021 etc)

Hi Archana,
It is given that the sequence is non-decreasing, which implies $$a_1\le\ a_2\le\ a_3\le\ ....\le\ a_n$$.
Now, we know that $$a_1+a_2+a_3+....+a_n=300n$$ and $$6a_1+a_2+a_3+....+a_n=400n$$. Therefore, we know that $$5a_1=100n\ =>\ a_1=20n$$
If we take n>15, then the value of $$a_{1\ }>\ 300$$. We know that the average is 300, and if $$a_{1\ }>\ 300$$, then a number other than $$a_{1\ }$$ must be less than 300 to get an average of 300, which is not possible since the sequence is non-decreasing ( $$a_{1\ }$$ must be the least valued term in the sequence).
I hope this helps! Please let me know if you have any other queries.