A sequence of positive numbers

[guerrero]

Apologies for using a screen shot as I could not figure out a way to type the question out .

OA C

[Matt@VeritasPrep]

NOTE: I'm assuming S2 is written incorrectly, and that it's supposed to say s_k = (s_(k-1))/3; in other words, that each term in the sequence is equal to the preceding term, divided by 3. Without that assumption, the problem seems unanswerable.

S1 gives us a relationship between two specific terms in the sequence. Let s5 = y and s4 = x. We have

y = x/(x-3)

Two variables, one equation - insufficient.

S2 defines the sequence. Since this describes the relationship between any two consecutive terms in the sequence, we can let sk = s5 = y and s(k-1) = s4 = x. We have

y = x/3

Again, two variables, one equation - insufficient.

Taking the two together, y = x/(x-3) and y = x/3, so

x/(x-3) = x/3
3x = x(x-3)
3x = x² - 3x
0 = x² - 6x
0 = x(x-6)

Since all the terms are positive, x is 6. That means the fourth term of the sequence is 6. Working backwards, if each term is equal to the preceding term divided by 3:

s4 = 6
s3 = 18
s2 = 72

So the two statements together are sufficient.

[guerrero]

thanks Mat , I could follow your approach . Also, I will let the author know about the flaw