Question

a1=2 si a3=5
r=?
S20=?

Answer 1

   
[tex]\displaystyle \\ \text{Se da: } \\ a_1=2~~ \text{si}~~ a_3=5 \\ \\ \text{Se cere: } \\ r=? \\ S_{20}=? \\ \\ \text{Rezolvare: } \\ \\ r = \frac{a_3 - a_1}{2} = \frac{5 - 2}{2} = \frac{3}{2} = \boxed{1,5 } \\ \\ a_{20} = a_1 + r(20-1) = 2 + 19\times 1,5 = 2+ 28,5 = \boxed{30,5} \\ \\ S_{20} = a_1 + a_2 + a_ 3 + \cdots + a_{20} = 2 + 3,5 + 5 + \cdots + 30,5 = \\ \\ = \frac{20(a_{20} + a_1)}{2} = \frac{20(30,5+2)}{2}=\frac{20\times32,5}{2}=10\times32,5=\boxed{325}[/tex]