A set has a series of numbers such as a that

A set has a series of numbers such as a that \(a_{n+2}= a_n + a_{n+1}\) . What is the value of \(a_7:a_5\)?

(1) The third term is 4. The 4th term is the sum of the previous two terms. If \(a_2=2\) and \(a_3=2\) you'll get one ratio for \(a_7:a_5\) but if \(a_2=1\) and \(a_3=3\) you'll get another ratio for \(a_7:a_5\). Not sufficient.

(2) \(a_4: a_5 = 3:5\) --> \(\frac{a_7}{a_5} = \frac{a_5+a_6}{a_5}=\frac{a_5+a_5+a_4}{a_5}=\frac{2*a_5+a_4}{a_5}=\frac{2*a_5}{a_5}+\frac{a_4}{a_5}=2+\frac{3}{5}\). Sufficient.

Answer: B.

P.S. You might find the following post helpful: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 (Writing Mathematical Formulas on the Forum)

Hi Guys,
This is my first post so please forgive me of all the formatting errors I am about to make

A set has a series of numbers such as a that a_{n+2}= a_n + a_{n+1} . What is the value of a_7:a_5?

(1) The third term is 4. The 4th term is the sum of the previous two terms. If a_2=2 and a_3=2 you'll get one ratio for a_7:a_5 but if a_2=1 and a_3=3 you'll get another ratio for a_7:a_5. Not sufficient.

(2) For the second part we can use Componendo mehthod
a4/a5 = 3/5
hence (a4+a5)/a5 = (3+5)/5 =8/5
a6/a5 = 8/5 apply again
(a6+a5)/a5 = (8+5)/5 =13/5
a7/a5 = 13/5

Componendo states that
if
a/b = c/d
(a+b)/c = (c+d)/d

other corollaries - Im not allowed to post links yet
I believe i need kudos to write mock tests so please help me about the same

Peace .

BTW- Bunuel - Big fan of ur solutions. reminds me of pure mathematics

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