Problem Solving

Okay, this book is from the official guide for gmat review 12th edition... it's one of the easier problems. I understand how to find the sequence, and i get the right answer which is e) 28 - it's just that i am thrown off by the equation.

how to solve for the value of a6
since a3 = 4 and a5 = 20...
the difference btwn these two numbers is 16 (notice how a4 is missing) so difference btwn each is 8.
one more up a6 = 28.

however, how would you plug this information into the sequence? (maybe i need to review my exponents again) but i am thrown off...

thanks for your help

given
An= (An-1 + An-2)/2 , for n>=3
2An = An-1 + An-2
now
2A6 = A5 + A4 --- (1)
2A5 = A4 + A3 --- (2)

By subtracting eq (2) from eq (1)
we get
2A6 - 2A5 = A5 + A4 - A4 - A3
2A6 = 3A5 - A3
2A6 = 3*20 - 4
A6 = 56/2 = 28

Hence the correct option is E

Hope this helps.

Hey
I'll try to do the same thing that Niket did, in a different and possibly easier way

You equation is:
An = [A(n-1) + A(n-2)]/2

A5 = (A4 + A3)/2
=> 20 = (A4 +4)/2
=> 40 = A4 + 4
=> A4 = 40-4
=> A4 = 36

Now, A6 = ( A5 + A4 )/2
=> A6 = (20 + 36)/2
=> A6 = 56/2
=> A6 = 28

Hence, Option E

My approach is like this:
By the given formula, it is evident that, a number in the series can be found out by taking the average(mean) of the previous two numbers.
a3 and a5 are given and we need to find a6.
To find a6, we need a4 and a5, as a6 = (a4+a5)/2.
a5 is already given. So let us try to find a4.

By our logic, a5 is nothing but (a3+a4)/2 => 20 = (a3+a4)/2
=> 40 = a3+a4 => 40 = 4 + a4 => a4 = 36

Then come back to a6,
a6 = (a4+a5)/2 = (36+20)/2 = 28

This approach is nothing new but same as Akash's approach. Here, a bit of articulation is added.
Howz that???

Due to time constraints in GMAT, I don't think there is a need to find a4 when you can simply eliminate it using my approach.

thank you all for your help, i was reallllly missing something on this question. not so difficult after all.