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#D3

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GHong14 Master | Next Rank: 500 Posts
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#D3

Post Fri Jun 03, 2011 11:21 am

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The sequence a1 a2....an is such that an = (an-1 + an-2)/2 for all n>=3. If a3=4 and a5=20, what is the value of a6.

12
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28

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Post Fri Jun 03, 2011 11:35 am
let a(n) means a subscript n
a(n) = (a(n-1) + a(n-2))/2
a3=4 and a5=20
if n=5; 20 = (a(4) + 4)/2 => a(4) = 36
Now a6 = (a4+a5)/2 = (20+36)/2 = 28
IMO E

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breakkgmat Junior | Next Rank: 30 Posts Default Avatar
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Post Sat Jun 04, 2011 1:03 am
We need to compute a4 in order to get the value of a6.
so, a5=a4+a3/2 or 20=a4+4/2 or 40=a4+4 or, a4=36.

So, a6 = a5+a4/2 = 20+36/2 = 56/2 = 28.Ans E.

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Post Sun Feb 11, 2018 9:39 pm
Hi All,

Sometimes the equation describing a sequence can be a bit 'layered'; here, we have to do a lot of little 'steps' to work through this sequence, but the 'math work' isn't too difficult (it's addition and division). Based on the given equation, the sequence can be thought of in the following way:

3rd term = (2nd term + 1st term)/2
4th term = (3rd term + 2nd term)/2
5th term = (4th term + 3rd term)/2
6th term = (5th term + 4th term)/2
Etc.

We're told that 3rd term = 4 and the 5th term = 20. We're asked for the value of the 6th term.

With the 3rd and 5th terms, we can figure out the value of the 4th term:

5th term = (4th term + 3rd term)/2
20 = (4th term + 4)/2
40 = 4th term + 4
36 = 4th term

And now that we have the 4th and 5th terms, we can figure out the 6th term:
6th term = (5th term + 4th term)/2
6th term = (20 + 36)/2
6th term = 56/2 = 28

Final Answer: E

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Rich

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Post Tue Feb 13, 2018 5:34 pm
GHong14 wrote:
The sequence a1 a2....an is such that an = (an-1 + an-2)/2 for all n>=3. If a3=4 and a5=20, what is the value of a6.

12
16
20
24
28
We see that:

a5 = (a4 + a3)/2

20 = (a4 + 4)/2

40 = a4 + 4

36 = a4

Now we can use a4 = 36 and a5 = 20 to obtain the value of a6:

a6 = (a5 + a4)/2

a6 = (20 + 36)/2

a6 = 56/2

a6 = 28

Answer: E

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