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# If the Sequence S has 100 terms what is the 83rd term

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Joined: 07 Jun 2004
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If the Sequence S has 100 terms what is the 83rd term  [#permalink]

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30 Sep 2010, 15:07
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If the Sequence S has 100 terms what is the 83 rd term

(1) Each term of S after the first term is 4 greater than the preceding term
(2) The 84th term of S is twice the 82nd term
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Joined: 02 Sep 2010
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30 Sep 2010, 15:26
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rxs0005 wrote:
If the Sequence S has 100 terms what is the 83d term

1 Each term of S after the first term is 4 greater than the preceding term

2 The 84th term of S is twice the 82nd term

(1) $$a_n = a_1 + 4(n-1)$$
Without knowing $$a_1$$, impossible to know $$a_{83}$$

(2) $$a_{84} = 2*a_{82}$$
All we know is that $$a_{83}$$ is the average of these two or $$1.5 * a_{82}$$, but this is still enough to calculate it.

(1+2) $$a_{84}=2*a_{82}$$
$$a_{84} = a_{82}+8$$
$$a_{82}+8=2*a_{82}$$
$$a_{82}=8$$
$$a_{83}=12$$

Sufficient

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30 Sep 2010, 15:47
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rxs0005 wrote:
If the Sequence S has 100 terms what is the 83d term

1 Each term of S after the first term is 4 greater than the preceding term

2 The 84th term of S is twice the 82nd term

Question: $$a_{83}=?$$

(1) $$a_n=a_{n-1}+4$$, for $$n>1$$. Not sufficient.

(2) $$a_{84}=2*a_{82}$$. Not sufficient.

(1)+(2) From (1) $$a_{84}=a_{83}+4$$ and $$a_{83}-4=a_{82}$$, from (2): $$a_{84}=2*a_{82}$$ --> $$a_{83}+4=2*(a_{83}-4)$$ --> $$a_{83}=12$$. Sufficient.

To elaborate more:
(1) says that the sequence is an arithmetic progression and gives the value of common difference --> so we have a linear relationship between any two terms.
(2) provides us with different linear relationship between 2 particular terms.

(1)+(2) We have two distinct linear equations with two unknowns --> we can get missing value.

Hope it helps.
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01 Oct 2010, 10:04
Took me about 8 minutes but I arrived at C once I realized I just had to see if I could work the information given into a solvable formula and then see which components I used to do so. This forum is proving very helpful already! Thanks all
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If the Sequence S has 100 terms what is the 83rd term  [#permalink]

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27 Aug 2014, 07:02
I solved this in 17 seconds once I realized the information given.

1) From the first statement, we realize we can write every term of the sequence in terms of $$S_1$$. $$S_2 = S_1+4$$, $$S_3 = S1 + 2(4)....S_{83} = S_1 + 82(4)$$. However, we still don't know $$S_1$$, so insufficient.

2) Clearly insufficient.

Together, we have a relationship between the two terms, both of which can be expressed in terms of $$S_1$$. That's one equation with one unknown. Therefore, we can easily solve for $$S_1$$ and therefore $$S_{83}.$$. Sufficient.

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Re: If the Sequence S has 100 terms what is the 83rd term  [#permalink]

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09 Aug 2017, 22:40
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Re: If the Sequence S has 100 terms what is the 83rd term   [#permalink] 09 Aug 2017, 22:40
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