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# Each term in sequence S is determined by multiplying the prior term by

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Math Expert
Joined: 02 Sep 2009
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Each term in sequence S is determined by multiplying the prior term by  [#permalink]

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02 Jun 2016, 11:54
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15% (low)

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76% (01:21) correct 24% (01:17) wrong based on 257 sessions

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Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. What is the 100th term of the sequence S?

(1) The sum of the first 2 terms is 15

(2) The first term of the sequence is 9

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Re: Each term in sequence S is determined by multiplying the prior term by  [#permalink]

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02 Jun 2016, 13:42
1
Let the first term = a , the second term will be equal to 2a/3. The third term = (2*2*a)/(3*3).
Thus the nth term = (a*2^(n-1))/(3^(n-1)). We are supposed to calculate the 100th term, so n = 100.
Stmt1 : Sum of first 2 terms = a + 2a/3 = 15. One equation one variable. we can solve this. Sufficient.
Stm2 : First term = a = 9. We already know n. Hence putting these values in the general equation of any term will give us the 100th term. Suff.

Hence D.
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Re: Each term in sequence S is determined by multiplying the prior term by  [#permalink]

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04 Jun 2017, 07:11
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Bunuel wrote:
Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. What is the 100th term of the sequence S?

(1) The sum of the first 2 terms is 15

(2) The first term of the sequence is 9

Target question: What is the 100th term of the sequence S?

Given: Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3.
In other words, if term_n = k, then term_(n+1) = (2/3)k
IMPORTANT: once we know the value of ANY term in the sequence, we can determine every other term in the sequence.

Statement 1: The sum of the first 2 terms is 15
Let x = term1
So, (2/3)x = term2
We can write: x + (2/3)x = 15
Since we COULD solve this equation for x, we COULD determine the value of the first term in the sequence, which means we COULD calculate every term in the sequence.
So, we COULD find the value of term100.
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT
NOTE: Of course, we're not going to actually calculate the 100th term, since doing so would be a waste of precious time

Statement 2: The first term of the sequence is 9
Now that we know the value of the first term in the sequence, we COULD calculate every term in the sequence.
So, we COULD find the value of term100.
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: Each term in sequence S is determined by multiplying the prior term by  [#permalink]

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05 Jun 2017, 02:17
As the question states that each term is determined by multiplying the prior term by 2 and dividing that product by 3.
so we can see series will be like x, 2x/3, 4x/9 and so on..
and it has a common ration of 2/3 so its a GP and to calculate nth term we have formula a*r^(n-1) where a is first term and r is the ratio
So we have the common ration and all we need is first term to find the 100th term.

Statement 1:
x+ 2x/3 = 15 and we get first term. Sufficient
Statement 2:
Directly tells about first term. Hence, it is also sufficient.

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Joined: 21 Aug 2015
Posts: 22
Re: Each term in sequence S is determined by multiplying the prior term by  [#permalink]

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05 Jun 2017, 02:17
As the question states that each term is determined by multiplying the prior term by 2 and dividing that product by 3.
so we can see series will be like x, 2x/3, 4x/9 and so on..
and it has a common ration of 2/3 so its a GP and to calculate nth term we have formula a*r^(n-1) where a is first term and r is the ratio
So we have the common ration and all we need is first term to find the 100th term.

Statement 1:
x+ 2x/3 = 15 and we get first term. Sufficient
Statement 2:
Directly tells about first term. Hence, it is also sufficient.

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Re: Each term in sequence S is determined by multiplying the prior term by  [#permalink]

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22 Oct 2018, 18:45
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Re: Each term in sequence S is determined by multiplying the prior term by   [#permalink] 22 Oct 2018, 18:45
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