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sequences

by kumard24 » Sat Mar 29, 2008 5:54 am
Sequence S is defined as Sn = 2Sn-1 – 2. If S1 = 3, then S10 – S9 =


2
120
128
250
256


We can use the formula to calculate the first 10 values of S:

S1 = 3 S2 = 2(3) – 2 = 4 S3 = 2(4) – 2 = 6
S4 = 2(6) – 2 = 10 S5 = 2(10) – 2 = 18 S6 = 2(18) – 2 = 34
S7 = 2(34) – 2 = 66 S8 = 2(66) – 2 = 130 S9 = 2(130) – 2 = 258
S10 = 2(258) – 2 = 514

S10 – S9 = 514 – 258 = 256.

This is driving me insane. what i dont understand is how does s2 =4. In particular where does the 3 come from?????
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Re: sequences

by Stuart@KaplanGMAT » Sat Mar 29, 2008 7:47 pm
kumard24 wrote:Sequence S is defined as Sn = 2Sn-1 – 2. If S1 = 3, then S10 – S9 =


2
120
128
250
256


We can use the formula to calculate the first 10 values of S:

S1 = 3 S2 = 2(3) – 2 = 4 S3 = 2(4) – 2 = 6
S4 = 2(6) – 2 = 10 S5 = 2(10) – 2 = 18 S6 = 2(18) – 2 = 34
S7 = 2(34) – 2 = 66 S8 = 2(66) – 2 = 130 S9 = 2(130) – 2 = 258
S10 = 2(258) – 2 = 514

S10 – S9 = 514 – 258 = 256.

This is driving me insane. what i dont understand is how does s2 =4. In particular where does the 3 come from?????
Sequences are defined by equations that link the terms.

S(n) is the nth term in the sequence (the "n" is usually subscripted). S(n+1) is the (n+1)th term in the sequence. S(n-1) is the (n-1)th term in the sequence.

For example, if S(5) is the nth term, then S(6) would be S(n+1) and S(4) would be S(n-1).

The sequence in this question is defined by the equation:

S(n) = 2S(n-1) – 2.

In English, this means that the current term is 2 times the previous term, minus 2.

So, if S(1) is 3, then S(2) is 2(3) - 2 = 6-2 = 4
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by kumard24 » Sun Mar 30, 2008 6:35 am
Perfect...it seems so obvious now!
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by subhakam » Wed Jan 23, 2013 8:39 pm
Stuart Kovinsky wrote:
kumard24 wrote:Sequence S is defined as Sn = 2Sn-1 � 2. If S1 = 3, then S10 � S9 =


2
120
128
250
256


We can use the formula to calculate the first 10 values of S:

S1 = 3 S2 = 2(3) � 2 = 4 S3 = 2(4) � 2 = 6
S4 = 2(6) � 2 = 10 S5 = 2(10) � 2 = 18 S6 = 2(18) � 2 = 34
S7 = 2(34) � 2 = 66 S8 = 2(66) � 2 = 130 S9 = 2(130) � 2 = 258
S10 = 2(258) � 2 = 514

S10 � S9 = 514 � 258 = 256.

This is driving me insane. what i dont understand is how does s2 =4. In particular where does the 3 come from?????
Sequences are defined by equations that link the terms.

S(n) is the nth term in the sequence (the "n" is usually subscripted). S(n+1) is the (n+1)th term in the sequence. S(n-1) is the (n-1)th term in the sequence.

For example, if S(5) is the nth term, then S(6) would be S(n+1) and S(4) would be S(n-1).

The sequence in this question is defined by the equation:

S(n) = 2S(n-1) � 2.

In English, this means that the current term is 2 times the previous term, minus 2.

So, if S(1) is 3, then S(2) is 2(3) - 2 = 6-2 = 4
What type of sequence is the above? If we want to find the formula of the sequence instead of finding value of each of them - how can that be done ? Is the above an exponential or arithmetic/liner sequence ??

All help greatly appreciated!
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