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In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that

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In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that

by VJesus12 » Fri May 08, 2020 8:13 am

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In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence?

(A) 3/5
(B) 5/8
(C) 8/5
(D) 5/3
(E) 9/2

[spoiler]OA=C[/spoiler]

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Re: In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that

by deloitte247 » Sun May 10, 2020 2:19 am
$$T_{n\ }=1+\left(reciprocal\ of\ T_{n-1}\right)$$
$$T_1=1$$
$$T_2=1+\left(reciprocal\ of\ T_1\right)$$
$$T_3=1+\left(reciprocal\ of\ T_2\right)$$
$$T_4=1+\left(reciprocal\ of\ T_3\right)$$
$$T_5=1+\left(reciprocal\ of\ T_4\right)$$
$$=>T_1=1$$
$$T_2=1+1=2$$
$$T_3=1+\frac{1}{2}=\frac{3}{2}$$
$$T_4=1+\frac{2}{3}=\frac{5}{3}$$
$$T_5=1+\frac{3}{5}=\frac{8}{5}$$

Answer = C
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