1 pt Find the first six terms of the recursively defined seq

(1 pt) Find the first six terms of the recursively defined sequence Sn = 2S^1/2n-1 /5 for n > 1, and s1 = 1.

Solution

S_n=(2*S_n-1^1/2)/5 n>1

S₁=1

for n=2 s₂=(2*S₁^1/2)/5=2*1/5=0.4

for n=3 s₃=(2*S₂^1/2)/5=2*sqrt(0.4)/5=0.2529

for n=4 s4=(2*S₃^1/2)/5=2*sqrt(0.2529)/5=0.2012

for n=5 s5=(2*S₄^1/2)/5=2*sqrt(0.2012)/5=0.1794

for n=6 s6=(2*S₅^1/2)/5=2*sqrt(0.1794)/5=0.1694

for n=7 s7=(2*S₆^1/2)/5=2*sqrt(0.1694)/5=0.1646