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.
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28
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cans
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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
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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Cans!!
Contact me about long distance tutoring!
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Cans!!
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breakkgmat
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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.
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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We see that: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
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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