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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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[Math Revolution GMAT math practice question]

The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n?

$$A. n$$
$$B. n^2$$
$$C. –n$$
$$D. -n^2$$
$$E. (n-1)^2$$

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Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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We see that the increment in the given sequence is:
From S1 to S2: +1 = 1^2
From S2 to S3: +4 = 2^2
From S3 to S4: +9 = 3^2
From S4 to S5: +16 = 4^2
...
Thus from Sn-1 to Sn = (n-1)^2.

Answer E
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Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n?

$$A. n$$
$$B. n^2$$
$$C. –n$$
$$D. -n^2$$
$$E. (n-1)^2$$

To answer any question of sequences, one needs to find a pattern so we keep looking at what we get when we canculate expressions like $$S_n - S_{n-1}$$

$$S_1 = 1$$
$$S_2 = 2$$ i.e. $$S_2 - S_{1} = 1= 1^1$$
$$S_3 = 6$$ i.e. $$S_3 - S_{2} = 4 = 2^2$$
$$S_4 = 15$$ i.e. $$S_4 - S_{3} = 9 = 3^2$$

i.e. $$S_n - S_{n-1} = (n-1)^2$$

Answer: Option E
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Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n?

$$A. n$$
$$B. n^2$$
$$C. –n$$
$$D. -n^2$$
$$E. (n-1)^2$$

If you don't spot a pattern, you can always TEST the answer choices

We want to find Sn - Sn-1
So, let's test a value of n.
How about n = 2
So, we want to find the value of S2 - S1
Well, we're told that S2 = 2 and S1 = 1
So, S2 - S1 = 2 - 1 = 1

So, when n = 2, the answer to the question (what is the value of Sn - Sn-1) is 1

Now we'll check the answer choices to see which one yields an OUTPUT of 1 when we input n = 2
A. n = 2. NO GOOD. We need an output of 1. ELIMINATE
B. n² = 2² = 4. NO GOOD. We need an output of 1. ELIMINATE
C. -n = -2 = -2. NO GOOD. We need an output of 1. ELIMINATE
D. -n² = -2² = -4. NO GOOD. We need an output of 1. ELIMINATE
E. (n - 1)² = (2 - 1)² = 1. perfect!!

Answer: E

Cheers,
Brent
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Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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=>

We begin by writing out the terms of the sequence:

S2-S1 $$= 2 -1 = 1=1^2$$
S3-S2 $$= 6 – 2 = 4 = 2^2$$
S4-S3 $$= 15 – 6 = 9 = 3^2$$
S5-S4 $$= 31-15 = 16 = 4^2$$

Following the above pattern gives
Sn-Sn-1 $$= (n-1)^2$$

Therefore, the answer is E.
Answer: E
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The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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Hello everyone!

Just to clarify.

Sn-Sn-1 $$= (n-1)^2$$

n = The position of the term, right?

I am getting confused with the symbols.

Kind regards!
VP  G
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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1
jfranciscocuencag wrote:
Hello everyone!

Just to clarify.

Sn-Sn-1 $$= (n-1)^2$$

n = The position of the term, right?

I am getting confused with the symbols.

Kind regards!

I would like to pitch in here.

Yes are correct, n is indeed the position of the term, because n is a positive integer and it is a part of this series.

s1 = 1, s2 = 2, s3= 6 ...

s2 = s2 - s1 = 1, 2-1 = 1^2

s3 = s3 - s2 = 6-2 = 4, which is nothing but (n-1)^2, (3-1)^2 = 4

Here n is the position of the integer in the series.

Kindly let me know if this helps.
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Intern  B
Joined: 16 Dec 2018
Posts: 10
Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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Ans is E.if u have problem with logic. Ucan just substute n =2 in ans

Posted from my mobile device Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If   [#permalink] 25 Jan 2019, 02:08
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# The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If

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