rohanGmat wrote:

The sequence A1 , A2 , ... is defined such that An+1 = \frac{An}{n+1} for all n>1 . How many terms of the sequence is greater than \frac{1}{2} ?

(1) A2 =5

(2) A1 −A2 =5

-Doubt --

1. We are specifically told tha the function is only valid for n>1, however the solution assumes that A2 = \frac{A1}{2} then shouldnt we say for all n>=1 ?

Also shouldnt the question say-- how many terms are (not is)

The sequence defined by some formula for all n>1, so it's valid for A2 (n=2>1).

The sequence A_1, A_2, ... is defined such that A_{n+1}=\frac{A_{n}}{n+1} for all n>1. How many terms of the sequence are greater than 1/2?Basically we have a sequence of numbers which is defined with some formula. For example:

A_{2}=\frac{A_{1}}{1+1},

A_{3}=\frac{A_{2}}{2+1},

A_{4}=\frac{A_{3}}{3+1}, ... The question asks: how many numbers from the sequence are greater than 1/2. Notice that if we knew ANY term of the sequence we would be able to get all the other terms/numbers and thus answer the question.

(1)

A_2=5. As discussed above this statement is sufficient as we can write down all the terms. For example:

A_{2}=\frac{A_{1}}{1+1}=5 -->

A_1=10.

A_{3}=\frac{A_{2}}{2+1}=\frac{5}{3}, and so on.

(2)

A_1-A_2=5 -->

A_1-\frac{A_{1}}{1+1}=5 --> we can solve for

A_1 and thus will have the same case of knowing one term. Sufficient.

Answer: D.

Hope it helps.

I am still not convinced. -- "The sequence defined by some formula for all n>1, so it's valid for A2 (n=2>1)" -- because in the function given you put n=1 to get A2 = A1/2 - yet in the next line we are told the function is only valid for all n>1.