Question

Sa se calculaze suma primilor 5 termeni ai unei progresi aritmetice , stiind ca a1 = 1 si a2 = 3 .

Answer 1

r=a2-a1=3-1=2 care este ratia

S5=n[2a1+(n-1)r] /2=5(2+8) /2=50/2=25
sau
1+3+5+7+9=25

Answer 2

$\displaystyle a_1=1,~a_2=3,~S_5=? \\ \\ a_2=3 \Rightarrow a_{2-1}+r=3 \Rightarrow a_1+r=3 \Rightarrow 1+r=3 \Rightarrow r=3-1 \Rightarrow r=2 \\ \\ S_5= \frac{2 \cdot 1+(5-1) \cdot 2}{2} \cdot 5 \\ \\ S_5= \frac{2+4 \cdot 2}{2} \cdot 5 \\ \\ S_5= \frac{2+8}{2} \cdot 5 \\ \\ S_5= \frac{10}{2} \cdot 5 \\ \\ S_5=5 \cdot 5 \\ \\ \boxed{S_5=25}$