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Math Expert V
Joined: 02 Sep 2009
Posts: 58311
In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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Difficulty:   15% (low)

Question Stats: 82% (01:40) correct 18% (01:48) wrong based on 100 sessions

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In a certain sequence, the term tn is defined as $$t_n = 3t_{n-1} - 2t_{n-2}$$ for all n > 2. If $$t_1 = -2$$ and $$t_2 = -1$$ , then $$t_4 =$$

A. -10
B. -8
C. -3
D. 1
E. 5

Kudos for a correct solution.

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Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
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Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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Bunuel wrote:
In a certain sequence, the term tn is defined as $$t_n = 3t_{n-1} - 2t_{n-2}$$ for all n > 2. If $$t_1 = -2$$ and $$t_2 = -1$$ , then $$t_4 =$$

A. -10
B. -8
C. -3
D. 1
E. 5

Kudos for a correct solution.

t3=3(t2)-2(t1)
=3(-1)-2(-2)
=-3+4
=1

t4=3(t3)-2(t2)
=3(1)-2(-1)
=3+2
=5

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Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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Answer = E = 5

Finding the value of$$t_3$$

$$t_3 = 3t_2 - 2t_1$$

$$t_3 = -3 +4 = 1$$

$$t_4 = 3t_3 - 2t_2 = 3 +2 = 5$$
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GMAT 1: 670 Q44 V38 Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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My answer is E.

T3 = -1*3 - (2*-2)= 1

T4=3*1 - (2*-2) = 5

I'll be happy if I got this right, I am terrible at sequences!~!
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Posts: 40
Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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Bunuel wrote:
In a certain sequence, the term tn is defined as $$t_n = 3t_{n-1} - 2t_{n-2}$$ for all n > 2. If $$t_1 = -2$$ and $$t_2 = -1$$ , then $$t_4 =$$

A. -10
B. -8
C. -3
D. 1
E. 5

Kudos for a correct solution.

T3 = 3(t2) - 2(t1) = 3(-1) - 2(-2) = 1
T4 = 3(t3) - 2(t2) = 3(1) - 2(-1) = 5

Option E
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Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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t3=3t2-2t1 = 1 (putting the value of t1 & t2, we can find out value of t3)
t4=3t3-2t2 = 5 (put the value of t2 &t3 in this and find out t4)

Hence answer is E

Thanks,
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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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Bunuel wrote:
In a certain sequence, the term tn is defined as $$t_n = 3t_{n-1} - 2t_{n-2}$$ for all n > 2. If $$t_1 = -2$$ and $$t_2 = -1$$ , then $$t_4 =$$

A. -10
B. -8
C. -3
D. 1
E. 5

Kudos for a correct solution.

$$t_3 = 3t_2 - 2t_1=3 *(-1) - 2*(-2)=1$$
$$t_4 = 3t_3 - 2t_2=3 *(1) - 2*(-1)=5$$

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Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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1
Bunuel wrote:
In a certain sequence, the term tn is defined as $$t_n = 3t_{n-1} - 2t_{n-2}$$ for all n > 2. If $$t_1 = -2$$ and $$t_2 = -1$$ , then $$t_4 =$$

A. -10
B. -8
C. -3
D. 1
E. 5

Kudos for a correct solution.

t4=3t3-2t2
t3=3t2-2t1=-3-2(-2)=1
Therefore, t4=3*1-2*-1=5. Asnwer=E
Math Expert V
Joined: 02 Sep 2009
Posts: 58311
Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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Bunuel wrote:
In a certain sequence, the term tn is defined as $$t_n = 3t_{n-1} - 2t_{n-2}$$ for all n > 2. If $$t_1 = -2$$ and $$t_2 = -1$$ , then $$t_4 =$$

A. -10
B. -8
C. -3
D. 1
E. 5

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment: Arithmetic_Recursion.png [ 18.11 KiB | Viewed 4836 times ]

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Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo  [#permalink]

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_________________ Re: In a certain sequence, the term tn is defined as tn = 3tn-1 - 2tn-2 fo   [#permalink] 09 Apr 2019, 22:17
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