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# In a certain sequence of positive integers, the term tn is given by th

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Math Expert
Joined: 02 Sep 2009
Posts: 64174
In a certain sequence of positive integers, the term tn is given by th  [#permalink]

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19 Mar 2020, 07:54
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Difficulty:

65% (hard)

Question Stats:

61% (02:59) correct 39% (03:12) wrong based on 41 sessions

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In a certain sequence of positive integers, the term $$t_n$$ is given by the formula $$t_n = 3(t_{n−2}) + 2(t_{n−1}) − 1$$ for all $$n ≥ 1$$. If $$t_6 = 152$$ and $$t_5 = 51$$, what is the value of $$t_2$$?

A. 1
B. 2
C. 3
D. 6
E. 17

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Re: In a certain sequence of positive integers, the term tn is given by th  [#permalink]

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19 Mar 2020, 10:09
Bunuel wrote:
In a certain sequence of positive integers, the term $$t_n$$ is given by the formula $$t_n = 3(t_{n−2}) + 2(t_{n−1}) − 1$$ for all $$n ≥ 1$$. If $$t_6 = 152$$ and $$t_5 = 51$$, what is the value of $$t_2$$?

A. 1
B. 2
C. 3
D. 6
E. 17

using given function formula first find t4 using
t6=3t4+2t5-1
t4= 17
then
t5=3t3+2t4-1
t3=6
t4=3t2+2t3-1
t2=2
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Re: In a certain sequence of positive integers, the term tn is given by th  [#permalink]

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21 Mar 2020, 14:51
Bunuel wrote:
In a certain sequence of positive integers, the term $$t_n$$ is given by the formula $$t_n = 3(t_{n−2}) + 2(t_{n−1}) − 1$$ for all $$n ≥ 1$$. If $$t_6 = 152$$ and $$t_5 = 51$$, what is the value of $$t_2$$?

A. 1
B. 2
C. 3
D. 6
E. 17

To solve for t(4), we can work backwards by first creating the equation:

t(6) = 3 x t(4) + 2 x t(5) - 1

152 = 3 x t(4) + 2 x 51 - 1

152 = 3 x t(4) + 101

51 = 3 x t(4)

17 = t(4)

Now, we can solve for t(3)::

t(5) = 3 x t(3) + 2 x t(4) - 1

51 = 3 x t(3) + 2 x 17 - 1

51 = 3 x t(3) + 33

18 = 3 x t(3)

6 = t(3)

Finally, we can solve for t(2):

t(4) = 3 x t(2) + 2 x t(3) - 1

17 = 3 x t(2) + 2 x 6 - 1

17 = 3 x t(3) + 11

6 = 3 x t(2)

2 = t(2)

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Re: In a certain sequence of positive integers, the term tn is given by th   [#permalink] 21 Mar 2020, 14:51