If a sequence is defined by \(a_n=(a_{n-1})\cdot(a_{n-2})+1\) for \(n \geq 3,\) and if \(a_1=1, a_2=1,\) what is the

[Vincen]

If a sequence is defined by \(a_n=(a_{n-1})\cdot(a_{n-2})+1\) for \(n \geq 3,\) and if \(a_1=1, a_2=1,\) what is the \(6^{th}\) term?

(A) 1
(B) 7
(C) 22
(D) 155
(E) 721


[spoiler]OA=C[/spoiler]

Source: Magoosh

[Jay@ManhattanReview]

If a sequence is defined by \(a_n=(a_{n-1})\cdot(a_{n-2})+1\) for \(n \geq 3,\) and if \(a_1=1, a_2=1,\) what is the \(6^{th}\) term?

(A) 1
(B) 7
(C) 22
(D) 155
(E) 721

[spoiler]OA=C[/spoiler]

Source: Magoosh

Plugging-in the value of n = 6, we get

\(a_6=(a_5)\cdot(a_4)+1\)

To get the value of \(a_6\), we will need the values of \(a_3, a_4, \&\ a_5\). So let's calculate them.

\(a_3=(a_2)\cdot(a_1)+1= 1\cdot1+1=2;\)
\(a_4=(a_3)\cdot(a_2)+1= 2\cdot1+1=3;\)
\(a_5=(a_4)\cdot(a_3)+1= 3\cdot2+1=7;\)

Thus, \(a_6=(a_5)\cdot(a_4)+1=7\cdot3+1=22\)

The correct answer: C

Hope this helps!

-Jay
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