Question

determinati al 100lea termren al sirului 3 7 11 15

Answer 1

a1=4x1-1=3     a2=4x2-1=7      a3=4x3-1=11        a4=4x4-1=15  atunci   a100=4x100-1=399

Answer 2

$\displaystyle 3,~7,~11,~15,...~~~~~~~~~~~~~~~~ a_{100}=? \\ a_1=3,~a_2=7,~a_3=11,~a_4=15 ,~... \\ r=7-3 \Rightarrow r=4 \\ a_{100}=a_{100-1}+r \Rightarrow a_{100}=a_{99}+r \Rightarrow a_{100}=a_1+99r \Rightarrow \\ \Rightarrow a_{100}=3+99 \cdot 4 \Rightarrow a_{100}=3+ 396 \Rightarrow \boxed{a_{100}=399}$