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05 Oct 2022, 08:17
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Difficulty:
85%
(hard)
Question Stats:
61% (03:22) correct
39%
(03:10)
wrong
based on 379
sessions
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For a certain sequence, \(t_n=-(t_{n-1}+1)^{-1}\) for all values of n such that \(n \geq {2}\). Given that \(t_1=1\), how much greater is the product of the first 200 values in this sequence than the sum of the first 200 values in this sequence?
A. 1
B. 68
C. 98
D. 105
E. 228
I found this question in our archives. The post was from 2004!!! Original author claims that it's from Manhattan GMAT (now Manhattan Prep). Give it a try!
A. 1
B. 68
C. 98
D. 105
E. 228
I found this question in our archives. The post was from 2004!!! Original author claims that it's from Manhattan GMAT (now Manhattan Prep). Give it a try!
05 Oct 2022, 23:43
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okay i tried to solve this but I am not able to get the answer
so when you plug in values for determining the terms in the sequence
you get ~ 1, -1/2, -2, 1...... gets repeating.
so the product of first three terms = -1 * -1/2 * -2 = 1
we need the value of product of first 200 terms so the product of first 198 terms will be 1 itself (1 * 99 = 1)
therefore the product of first 200 terms will be 1 * 1 * -1/2 = -1/2
now for the sum of first three numbers we get 1 - 1/2 - 2 = -3/2
the sum of first 98 numbers will be (-3/2)* 99 = - 297/2
to find the sum of 200 numbers will be -297/2 + 1 - 1/2 = -148
but i'm not able to get the answer with this method.
Could you help me find where i'm wrong?
so when you plug in values for determining the terms in the sequence
you get ~ 1, -1/2, -2, 1...... gets repeating.
so the product of first three terms = -1 * -1/2 * -2 = 1
we need the value of product of first 200 terms so the product of first 198 terms will be 1 itself (1 * 99 = 1)
therefore the product of first 200 terms will be 1 * 1 * -1/2 = -1/2
now for the sum of first three numbers we get 1 - 1/2 - 2 = -3/2
the sum of first 98 numbers will be (-3/2)* 99 = - 297/2
to find the sum of 200 numbers will be -297/2 + 1 - 1/2 = -148
but i'm not able to get the answer with this method.
Could you help me find where i'm wrong?
06 Oct 2022, 06:33
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This pattern keeps repeating:
1, -1/2, -2,...
This shows that the product of consecutive three terms is 1. So, in 200 terms, the product of first 198 terms would be 1. The product of next two terms (following the pattern) will be -1/2. Hence: P=-1/2=-0.5
We can find the sum using the same pattern as above. The sum of first three terms comes out to be -3/2. This pattern would get repeated till the 198th term, which means it will be repeated 198/3=66 times. Add the leftover 2 terms to find the total sum:
Sum = -3/2(66)+1-1/2=-98.5
P-S=-0.5-(-98.5)-=98
Please feel free to point out any mistakes!
1, -1/2, -2,...
This shows that the product of consecutive three terms is 1. So, in 200 terms, the product of first 198 terms would be 1. The product of next two terms (following the pattern) will be -1/2. Hence: P=-1/2=-0.5
We can find the sum using the same pattern as above. The sum of first three terms comes out to be -3/2. This pattern would get repeated till the 198th term, which means it will be repeated 198/3=66 times. Add the leftover 2 terms to find the total sum:
Sum = -3/2(66)+1-1/2=-98.5
P-S=-0.5-(-98.5)-=98
Please feel free to point out any mistakes!
