Sequence DS question

[Sulman Raja]

Hi Guys:

I came acorss this sequence question. I would like to see your explanation on this.

The infinite sequence , ,…,,… is such that , , , , and  for  n > 4. What is the sum of the first 98 terms of the sequence?

(1)  x = 5
(2)  y + z = 2

[Matt P]

Well, obviously if we know x, y, and z, then the answer is solvable..

So that tells us that it must be C or E. (Since there's no way we could solve this without having information of X or (Y, Z)).

To determine if statement 1+2 are enough, let's figure out if y and z are always combined; y+z=2 may not be useful enough, since we may need information about each of the values.

98 terms means 96 terms + 2 terms. The 96 will be easily summed with (1) + (2) since groups of 4 will not distinguish between y and z.

But since the two other terms are x and y, we can't solve the question, as we don't know the value for y.

Thus the answer should be (E).

If not, I guess I'll be embarrassed :P

[Sulman Raja]

Hey Matt:

That is the correct answer.  I like your explanation on how you narrowed down your choices to C and E. However, it is not clear on how you reached to this statement from the question stem:

98 terms means 96 terms + 2 terms. The 96 will be easily summed with (1) + (2) since groups of 4 will not distinguish between y and z.

This is the right approach, but I'm curious to know how you got there.  If you don't mind :)

Sulman

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[Vaibhav Sinha]

Hi Sulman,

Let me fill in. I hope, its clear that the answer choices relevant here are only C and E. 

Lets take C and understand how it is insufficient.

If we know value of X and Y+Z, and we have 3 (given), we will get the first 4 terms of the series i.e, a1( which is x=5, from statement 1) , a2 (which is y) , a3 (which is z), a4 (which is 3, given). Using statement 2, this sum would be, a1+a2+a3+a4=5+(2)+3= 10. 

And we also know, that the series is repeated after every fourth term.(since given, An=An-4, where n>4)

Therefore,

a5=a1

a6=a2

a7=a3

a8=a4

We have, a5+a6+a7+a8 = a1+a2+a3+a4= 10. 

Therefore, for any multiple of 4x terms, we can find the value of summation as 10x. But question stem asks for 98th term (which is not a multiple of 4). 

The closest multiple of 4 is 96. Therefore, the series expression, beginning from 96 (24x 4), can be written as,

96th term  = a4

97th term = x (we know this value from statement 1 i.e. 5)

98th term = y (WE DONT KNOW THIS VALUE since We know only y+z) 

Hence we can't derive an answer from the two statements. Therefore, E is the correct answer.

Hope it explains your query (whew)

Vaibhav.