Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. What is the 100th term of the sequence S?

(1) The sum of the first 2 terms is 15

(2) The first term of the sequence is 9
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Target question: What is the 100th term of the sequence S?

Given: Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3.
In other words, if term_n = k, then term_(n+1) = (2/3)k
IMPORTANT: once we know the value of ANY term in the sequence, we can determine every other term in the sequence.

Statement 1: The sum of the first 2 terms is 15
Let x = term1
So, (2/3)x = term2
We can write: x + (2/3)x = 15
Since we COULD solve this equation for x, we COULD determine the value of the first term in the sequence, which means we COULD calculate every term in the sequence.
So, we COULD find the value of term100.
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT
NOTE: Of course, we're not going to actually calculate the 100th term, since doing so would be a waste of precious time

Statement 2: The first term of the sequence is 9
Now that we know the value of the first term in the sequence, we COULD calculate every term in the sequence.
So, we COULD find the value of term100.
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT


Answer:

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

As the question states that each term is determined by multiplying the prior term by 2 and dividing that product by 3.
so we can see series will be like x, 2x/3, 4x/9 and so on..
and it has a common ration of 2/3 so its a GP and to calculate nth term we have formula a*r^(n-1) where a is first term and r is the ratio
So we have the common ration and all we need is first term to find the 100th term.

Statement 1:
x+ 2x/3 = 15 and we get first term. Sufficient
Statement 2:
Directly tells about first term. Hence, it is also sufficient.

D is the correct answer.