Manhattan CAT5, need clarification from Instructors

[nagm]

In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is 3.
(2) The second to last term is 3**10.

1- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3- Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
4- EACH statement ALONE is sufficient.
5- Statements (1) and (2) TOGETHER are NOT sufficient.

We can write a formula of this sequence: Sn = 3Sn-1

(1) SUFFICIENT: If we know the first term S1 = 3, the second term S2 = (3)(3) = 9.
The third term S3 = (3)(9) = 27
The fourth term S4 = (3)(27) = 81

(2) INSUFFICIENT: We can use this information to find the last term and previous terms, however, we don't know how many terms there are between the second to last term and the fourth term.
The correct answer is A

My thinking:
Say first term is 3
This is a Geometric Progression
3, 9, 27, 81, ........., 3**(n-1)

Ratio of 2nd to last term is 3**10
so (3**(n-1))/(3**2) = 3**10
that gives me n=11
The correct answer should be D

[nagm]

OOPS correct explaination is giveb below
My thinking:
Say first term is 3
This is a Geometric Progression
3, 9, 27, 81, ........., 3**(n-1)

Ratio of 2nd to last term is 3**10
so (3**(n-1))/(3**2) = 3**10
that gives me n=13
The correct answer should be D

[viksnme]

OOPS correct explaination is giveb below
My thinking:
Say first term is 3
This is a Geometric Progression
3, 9, 27, 81, ........., 3**(n-1)

Ratio of 2nd to last term is 3**10
so (3**(n-1))/(3**2) = 3**10
that gives me n=13
The correct answer should be D

Hi nagm, if you consider statement 2, solving that gives us 2 unknowns, the first term and the number of terms. If the first term were given, we could have solved for the 4th term. You have assumed the series starts with 3 but statement 2 does not specify that, hence, it is insufficient.
If the second last term is 3**10, last term is 3**11. Let 'a' be the first term, hence using the formula-
Tn=a*R**(n-1) = 3**11 = a * 3**n hence we need either a or n to solve for T4.

[RonPurewal]

Ratio of 2nd to last term is 3**10
so (3**(n-1))/(3**2) = 3**10
that gives me n=11
The correct answer should be D

the problem is here.

you're misinterpreting the phrase 'second to last term'; apparently, you interpreted this as if it means 'the RATIO of the second term to the last term'. unfortunately, that's not what it means: 'second to last' is an (idiomatic) expression that means 'the term before the last term'. in other words, if there are N terms in the sequence, then 'the second to last term' is the (N-1)th term.

we should have hyphenated that phrase, though: it should read 'second-to-last'. that edit would make it more clear that we're talking about just one term - the one that comes before the last one.