Question

Se considera progresia aritmetica (an)n>1,in care a1=2 si a3=8.Sa se calculeze suma primilor 10 termeni ai progresiei.Vreau rezolvarea pe pasi,ms

Answer 1

[tex]a_1=2\\ a_3=8\\ a_1+2r=8\\ 2+2r=8\\ 2r=6\Rightarrow r=3\\ S_{10}=\frac{(a_1+a_{10})\cdot 10}{2}\\ S_{10}=(a_1+a_1+9r)\cdot 5\\ S_{10}=(2\cdot 2+9\cdot 3)\cdot 5\\ S_{10}=(4+27)\cdot 5\\ S_{10}=31\cdot 5\Rightarrow S_{10}=155[/tex]