Question

În progresia aritmetică (an) cu n mai mare egal cu 1, se știe că a1+a5+a9+a13=28. Calculați suma primilor 13 termeni ai progresiei. Haideti ca îmi pic bacu' :))

Edit: Lasati baieti ca am rezolvat, mersi frumos pentru nimic. Daca cineva e curios de rezolvare, poate sa ma intrebe.

Answer 1

 

$\displaystyle\bf\\a_1+a_5+a_9+a_{13}=28\\\\a_5=a_1+4r\\a_9=a_1+8r\\a_{13}=a_1+12r\\\\a_1+a_5+a_9+a_{13}=28\\\\a_1+(a_1+4r)+(a_1+8r)+(a_1+12r)=28\\\\4a_1+24r=28~~~\Big|:4\\\\\boxed{\bf~a_1+6r=7}\\\\a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a_{10}+a_{11}+a_{12}+a_{13} =\\\\=a_1+(a_1+r)+(a_1+2r)+(a_1+3r)+...+(a_1+12r)=\\\\=13a_1 + (r+2r+3r+...+12r) =\\\\= 13a_1 + r(1+2+3+...+12) =\\\\= 13a_1 + r\times\frac{12(12+1)}{2}=\\\\=13a_1+r\times6\times13=\\\\=13(a_1+6r)=\\\\=13\times7=\boxed{\bf91}$