Question

Scrieti primii cinci termrni ai progresiei aritmetrice (an) daca: a1=5,r=2 b) a1=-2,r=3

Answer 1

$\displaystyle a).a_1=5,~r=2 \\ a_2=a_{2-1} +r \Rightarrow a_2=a_1+r \Rightarrow a_2=5+2 \Rightarrow a_2=7 \\ a_3=a_{3-1}+r \Rightarrow a_3=a_2+r \Rightarrow a_3=a_1+2r \Rightarrow a_3=5+2 \cdot 2 \Rightarrow \\ \Rightarrow a_3=5+4 \Rightarrow a_3=9 \\ a_4=a_{4-1}+r \Rightarrow a_4=a_3+r \Rightarrow a_4=a_1+3r \Rightarrow a_4=5+3 \cdot 2 \Rightarrow\\ \Rightarrow a_4=5+6 \Rightarrow a_4=11$
$\displaystyle a_5=a_{5-1}+r \Rightarrow a_5=a_4+r\Rightarrow a_5=a_1+4r\Rightarrow a_5=5+4 \cdot 2 \Rightarrow \\ \Rightarrow a_5=5+8 \Rightarrow a_5=13 \\ 5,7,9,11,13,...$
$\displaystyle b).a_1=-2,~r=3 \\ a_2=a_1+r \Rightarrow a_2=-2+3 \Rightarrow a_2=1 \\ a_3=a_1+2r \Rightarrow a_3=-2+2 \cdot 3 \Rightarrow a_3=-2+6 \Rightarrow a_3=4 \\ a_4=a_1+3r \Rightarrow a_4=-2+3 \cdot 3 \Rightarrow a_4=-2+9 \Rightarrow a_4=7 \\ a_5=a_1+4r \Rightarrow a_5=-2+4 \cdot 3 \Rightarrow a_5=-2+12 \Rightarrow a_5=10 \\ -2,1,4,7,10,...$