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Linear Sequences

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jillian.sala
 Post subject: Linear Sequences
 Post Posted: Sun Apr 26, 2009 5:35 pm 
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Course Students


Posts: 1
I'm studying the MGMAT flash cards and am having trouble with linear sequences.

The question is, "What is the 25th term of this sequence?"

S(sub n) = S(sub n-1) -10 and S(sub 3) = 0

I don't understand how I find the direct sequence formula for this. Is this somewhere in the strategy guides?

Thanks!
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RonPurewal
 Post subject: Re: Linear Sequences
 Post Posted: Sun May 03, 2009 4:56 am 
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ManhattanGMAT Staff


Posts: 7146
jillian.sala wrote:
I'm studying the MGMAT flash cards and am having trouble with linear sequences.

The question is, "What is the 25th term of this sequence?"

S(sub n) = S(sub n-1) -10 and S(sub 3) = 0

I don't understand how I find the direct sequence formula for this. Is this somewhere in the strategy guides?

Thanks!


hey -

you don't need to find a direct formula.

in this problem, as in many other sequence problems, you should just LOOK FOR A PATTERN, and then extrapolate the pattern that you find.

with the data you've posted:
3rd term = 0
4th term = -10
5th term = -20
6th term = -30
etc.

it's pretty clear what's going on here.

the 25th term is twenty 10's below the 5th term:
25th term = 5th term - (20)(10) = -20 - 200
= -220

trying to find an explicit formula here is pretty much a waste of time.
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santhosh.ren
 Post subject: Re: Linear Sequences
 Post Posted: Wed Dec 22, 2010 3:13 pm 
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Students


Posts: 1
The formula is -
S(n) = 20n + k, where k is a constant.
nth term = difference in terms * n + k, where k is a constant.

So, in this sequence, the first step is to find the difference by which the terms are increasing/decreasing. The difference here between terms is 20.

So, S(n) = 20n + k. To find k, substite one of the given terms in the sequence.
-2 = 20(1) + k (since -2 is the first term in the sequence, n=1)
k = -22.

So, the formula to find the nth number in this series would be:
S(n)=20n-22.
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jnelson0612
 Post subject: Re: Linear Sequences
 Post Posted: Sun Dec 26, 2010 10:19 am 
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ManhattanGMAT Staff


Posts: 1857
santhosh, please go back and read Ron's explanation. Your formula is not going to yield the correct result.

_________________
Jamie Nelson
ManhattanGMAT Instructor
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