How do you find the first five terms given #a_1=3/4#, #a_(n+1)=(n^2+1)/n*a_n#?

1 Answer
Shwetank Mauria
Jan 13, 2017

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

Explanation:

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,............}#

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