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# What is the 1st term in sequence S? (1) The 3rd term of S is

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What is the 1st term in sequence S? (1) The 3rd term of S is [#permalink]

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02 Mar 2004, 10:36
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What is the 1st term in sequence S?
(1) The 3rd term of S is 4.
(2) The 2nd term of S is three times the 1st, and the 3rd term is four times the 2nd.

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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Joined: 30 Aug 2003
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02 Mar 2004, 10:46
both are needed..
first term is suppose x and 2nd term is 3x and 3rd is 4(3x)=12x
from 1st stemt 12x=4 .. can get the 1st term of seq
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shubhangi

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04 Mar 2004, 10:54
(1) is no help in finding the first term of S --- INSUFF
For example, the following sequences each have 4 as their third term, yet they have different first terms:

0, 2, 4
-4, 0, 4

This eliminates choices A and D.
Although (2) contains a lot of information, it also is not sufficient. For example, the following sequences each satisfy (2),
yet they have different first terms:

1, 3, 12
3, 9, 36

This eliminates B.
Next, we consider (1) and (2) together. From (1), we know "the 3rd term of S is 4." From (2), we know "the 3rd term is four times the 2nd." This is equivalent to saying the 2nd term is 1/4 the 3rd term: (1/4)4 = 1. Further, from (2), we know "the 2nd term is three times the 1st." This is equivalent to saying the 1st term is 1/3 the 2nd term: (1/3)1 = 1/3. Hence, the first term of the sequence is fully determined: 1/3, 1, 4.

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

04 Mar 2004, 10:54
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