Question

Cum calculez a1+a2+a3+....+an daca mi se da doar an=3n-2

Answer 1

$a_1+a_2+a_3+...+a_n = S_n \\ \\ S_n = \dfrac{(a_1+a_n)\cdot n}{2} \\ \\ a_n = 3n-2 \Rightarrow a_1 = 3\cdot 1-2 \Rightarrow a_1 = 1 \\ \\ \Rightarrow S_n = \dfrac{\Big(1+(3n-2)\Big)\cdot n}{2} \Rightarrow S_n = \dfrac{(3n-1)\cdot n}{2} \Rightarrow S_n = \dfrac{3n^2-n}{2} \Rightarrow \\ \\ \Rightarrow \boxed{a_1+a_2+a_3+...+a_n= \dfrac{3n^2-n}{2}}$