How do you find the first five terms given $a_{1} = \frac{3}{4}$ $a_1=3/4$ , $a_{n + 1} = \frac{n^{2} + 1}{n} \cdot a_{n}$ $a_(n+1)=(n^2+1)/n*a_n$ ?

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Answer 1 · 2017-01-13T06:01:02

Sequence is ${3/4,3/2,15/4,25/2,425/8,............}$

As $a_1=3/4$

$a_2=a_(1+1)=(1^2+1)/1*a_1=2*3/4=3/2$

$a_3=a_(2+1)=(2^2+1)/2*a_2=5/2*3/2=15/4$

$a_4=a_(3+1)=(3^2+1)/3*a_3=10/3*15/4=25/2$

$a_5=a_(4+1)=(4^2+1)/4*a_3=17/4*25/2=425/8$

and sequence is ${3/4,3/2,15/4,25/2,425/8,............}$

How do you find the first five terms given a_1=3/4a1=34a_1=3/4, a_(n+1)=(n^2+1)/n*a_nan+1=n2+1n⋅ana_(n+1)=(n^2+1)/n*a_n?