Question

Fie an o progresie aritmetica. Sa se calculeze S30 dacă a7+a14+a16+a25=80.

Answer 1

$a_7+a_{14}+a_{16}+a_{25}=80\\ \\ a_1+6r+a_1+13r+a_1+15r+a_1+24r=80\\ \\ \Rightarrow 4a_1+58r=80 \ |:2 \Rightarrow a_1+29r=40 \\ \\ S_{30}=\frac{n(a_1+a_n)}{2}\\ \\ S=\frac{n(a_1+a_1+(n-1)r}{2}\\ \\S=\frac{30(2\cdot a_1+29\cdot r)}{2}\\ \\ S=15\cdot 40=600$