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Sequence S is such that Sn [#permalink]
Expert's post 00:00

Question Stats: 68% (02:04) correct 31% (02:31) wrong based on 44 sessions
Sequence S is such that Sn = Sn-1 + 3/2 and S1 = 2

Sequence A is such that An = An-1 - 1.5 and A1 = 18.5

 Quantity A Quantity B The sum of the terms in S from S1 to S13, inclusive The sum of the terms from in A from A1 to A13, inclusive

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for the correct answer AND explanation
[Reveal] Spoiler: OA

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Re: Sequence S is such that Sn [#permalink]
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Formula given to us:

$$Sn = Sn-1 +1.5; s1 = 2 and An = An-1 - 1.5; A1 = 18.5$$

For the first sequence
Each subsequent value of $$s$$ is greater by $$1.5$$ For solving the question we need to calculate the sum of first 13 terms
we have the 1st term as $$2$$. There remains $$12$$ more terms. We know that there is an increase of $$1.5$$ per term hence there is a total increase of $$12 * 1.5 = 18$$
Last term of the sequence = $$2+18 = 20$$

Since the sequence is equally spaced avg = $$\frac{2 +20}{2} = 11$$
There are a total of $$13$$ terms hence sum of the sequence = $$11* 13 = 143$$

For the second sequence
Each subsequent value of A is less by $$1.5$$ For solving the question we need to calculate the sum of first $$13$$ terms
we have the 1st term as $$18.5$$ There remains $$12$$ more terms. We know that there is a decrease of $$1.5$$ per term hence there is a total decrease of $$12 * 1.5 = 18$$
Last term of the sequence = $$18.5 - 18 = 0.5$$
Since the sequence is equally spaced avg = $$\frac{0.5 +18.5}{2} = 9.5$$
There are a total of $$13$$ terms hence sum of the sequence = $$9.5* 13 = 123.5$$
Option A
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Re: Sequence S is such that Sn [#permalink]
option A Manager Joined: 22 Feb 2018
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Re: Sequence S is such that Sn [#permalink]
1
KUDOS

A:
Sn = Sn-1 + 3/2 and S1 = 2
Sn = a + (n-1)d
a = S1 (the first element in the sequence)
d = Sn - Sn-1 = 3/2 (distance between two following elements in this kind of sequence which every new element is made by adding a constant value to it’s previous element)

Sn = 2 + (n-1) * 3/2 = 2 + 3/2*n - 3/2 = 1/2 + 3/2*n
Sum of the terms in S from s1 to S13, inclusive = (S1+ S13) *n / 2 = (2+20)*13/2=11*13 = 143
S1 = 2
S13 = 1/2 + 3/2*13 = 20

B:
The sum of the terms in A from A1 to A13, inclusive =

An = An-1 -1/2 and S1 = 18.5
Sn = a + (n-1)d
a = A1 (the first element in the sequence)
d = Sn - Sn-1 = -1.5 (distance between two following elements in this kind of sequence which every new element is made by adding a constant value to it’s previous element)

An = 18.5 + (n-1) * (-1.5) = 18.5 - 3/2*n + 3/2 = 20- 3/2*n

Sum of the terms in A from A1 to A13, inclusive = (A1+A13) *n / 2 = (18.5 + 0.5)*13/2=19*13/2 = 123.5
A1 = 18.5
A13 = 20-3/2*13 = 1/2

So A is bigger.
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Last edited by Fatemeh on 28 Nov 2018, 19:32, edited 1 time in total.
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Re: Sequence S is such that Sn [#permalink]
I didnt get it Re: Sequence S is such that Sn   [#permalink] 25 Oct 2018, 06:06
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