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Can you explain this problem?

Expert replies
by yumi2012 » Sun Nov 17, 2013 11:24 pm
Thanks in advance!
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Source: — Problem Solving |

by Uva@90 » Sun Nov 17, 2013 11:33 pm
Given that T1 = 23
and Tn = T(n-1) - 3
To Find:
For what n
Tn = -4

T1 = 23
T2 = 23-3
T3 = 23-3-3 or 23 - 2*(3)
T4 = 23 - 3*(3)
From the above sequence we know that
Tn = T1 - (n-1)*3 = -4
=> 23- (n-1)*3 = -4
n-1 = 9
N = 10
Hence Answer is C

Hope it helps you

Regards,
Uva.
Known is a drop Unknown is an Ocean
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by [email protected] » Mon Nov 18, 2013 12:05 am
Hi yumi2012,

Uva@90 has provided a solid explanation for the "math" behind this question. The most important part is to understand that the sequence is decreasing by 3 with every term. We're given the value of the first term (23) and we're asked to figure out which term = -4.

If you can't see the "algebra" behind this question, then you could just "brute force" the sequence. Here's how:

1st = 23
2nd = 20
3rd = 17
4th = 14
5th = 11
6th = 8
7th = 5
8th = 2
9th = -1
10th = -4

Final Answer: C

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by GMATGuruNY » Mon Nov 18, 2013 4:08 am
Alternate approach:

T(n) = T(n) - 3.

According to the formula above, each term is 3 less than the preceding term.
The result is an EVENLY SPACED SET.

To count the number of integers in an evenly spaced set, use the following formula:
(biggest - smallest)/interval + 1.
The interval is the distance between successive terms.

Here, the interval is 3, since each term is 3 less than the preceding term.
Since the biggest term = 23 and the smallest term = -4, we get:
Number of terms = (biggest - smallest)/interval + 1 = [23 - (-4)]/3 + 1 = 10.

The correct answer is C.
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