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Updated on: 19 Feb 2020, 08:22
Originally posted by BrentGMATPrepNow on 18 Feb 2020, 07:20.
Last edited by BrentGMATPrepNow on 19 Feb 2020, 08:22, edited 1 time in total.
Last edited by BrentGMATPrepNow on 19 Feb 2020, 08:22, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
67% (02:47) correct
33%
(03:04)
wrong
based on 198
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In a certain the sequence, \(t_n=\frac{t_{n−1}}{t_{n−2}}\) for \(n > 2\). If \(t_1=3\) and \(t_2=5\), then what is the product of the first 54 terms of the sequence?
A) 3/5
B) 1/3
C) 1
D) 5/3
E) 5
A) 3/5
B) 1/3
C) 1
D) 5/3
E) 5
18 Feb 2020, 12:03
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t1=3
t2=5
t3=5/3
t4=1/3
t5=1/5
t6=3/5
Repeat again
t7=3
t8=5
54/6=9
t1*t2.....*t54=(t1*t6)^9
t1*...t6=1
So....1^9=1
So 1
[size=80][b][i]Posted from my mobile device[/i][/b][/size]
t2=5
t3=5/3
t4=1/3
t5=1/5
t6=3/5
Repeat again
t7=3
t8=5
54/6=9
t1*t2.....*t54=(t1*t6)^9
t1*...t6=1
So....1^9=1
So 1
[size=80][b][i]Posted from my mobile device[/i][/b][/size]
18 Feb 2020, 22:27
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Step1:
Finding the pattern:
t1 = 3, t2 = 5, t3=5/3, t4 = 1/3, t5 = 1/5, t6 = 3/5
t7 = 3, t8 = 5.... so on..
After 6th term first term repeats itself
There is a cycle of 6 terms.
Step 2:
Product of first six terms is 1.
Step 3:
Finding the product of 54 terms
For 54 terms there will be 9 cycles of 6 terms each, having product of 1, total product = 1
C is correct
Finding the pattern:
t1 = 3, t2 = 5, t3=5/3, t4 = 1/3, t5 = 1/5, t6 = 3/5
t7 = 3, t8 = 5.... so on..
After 6th term first term repeats itself
There is a cycle of 6 terms.
Step 2:
Product of first six terms is 1.
Step 3:
Finding the product of 54 terms
For 54 terms there will be 9 cycles of 6 terms each, having product of 1, total product = 1
C is correct
