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# If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Location: Pune, India
Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-  [#permalink]

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24 Jan 2019, 05:58
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jfranciscocuencag wrote:
Bunuel wrote:
anilnandyala wrote:
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

a) 1,800

b) 1,845

c) 1,890

d) 1,968

e) 2,016

Hello!

COuld someone please clarify to me how do we get to the following?

$$s_1+6(n-1)$$

Kind regards!

Given $$S_n = S_{n-1} + 6$$
Every subsequent term is 6 more than the previous term. So it is an Arithmetic Progression with common difference 6. In an arithmetic progression,

$$T_n = a + (n - 1)*d$$
where a is the first term, $$T_n$$ is the nth term and d is the common difference.

So $$S_n = s_1 + (n - 1)*6$$

For more, check: https://www.veritasprep.com/blog/2012/0 ... gressions/
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Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-  [#permalink]

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24 Jan 2019, 09:25
Thank you very much VeritasKarishma !

Now is very clear.
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If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-  [#permalink]

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24 Jan 2019, 10:54
anilnandyala wrote:
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6, ..., what is the sum of all terms in the set {S13, S14, ..., S28}?

A. 1,800
B. 1,845
C. 1,890
D. 1,968
E. 2,016

Calculate the number of terms correctly

S13 ........ S28 will be 16 terms, [a+b-1] , one can calculate S13 = a + 12d and S28 = a + 27d

Here a= 6 and d = 6

After that, this series will be a series of multiple of 6
$$S_n$$ = n/2 [first term + last term], Sum of n terms in a series

$$S_{16}$$ = 16/2 [78 + 168]

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If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-   [#permalink] 24 Jan 2019, 10:54

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