Oblicz trzynasty wyraz ciągu arytmetycznego.
a) 0, 4, 8, 12, ...
b) 1, 1 + √2/2, 1+ √2, ...
c) 4 i 1/3, 3 i 2/3, 3, ...
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a)
b)
c)
a)
r=4-0=4
a(n)=0+4(n-1)=4n-4
a₁₃=4·13-4=52-4=48
b)
r=1+0,5√2-1=0,5√2
a(n)=1+0,5√2(n-1)=0,5n√2+1-0,5√2
a₁₃=0,5·13·√2+1-0,5√2=6,5√2+1-0,5√2=6√2+1
c)
r=3²/₃-4¹/₃=-²/₃
a(n)=4¹/₃-²/₃(n-1)=-²/₃n+5
a₁₃=-²/₃·13+5=-8²/₃+5=-3²/₃