Question

Se considera o progresie aritmetica ($a_{n}$ )$n \geq _{1}$ cu proprietatea ca $a_{6} + a_{9} + a_{12} + a_{15} =50$. Calculati suma primilor 20 termeni.

Answer 1

a6+a9+a12+a15=50
a1+5r+a1+8r+a1+11r+a1+14r=50
4a1+38r=50 adica 2a1+19r=25
S20= (a1+a20)*20/2=(a1+a1+19r)*10=(2a1+19r)*10=25*10=250