Question

calcula la suma de los primeros 12 términos an = - 1/2 + 3/4 n


Doy corona ​

Answer 1

Respuesta:

$a_1 = -\frac{1}{2} +\frac{3}{4} .(1)\\a_2 = -\frac{1}{2} +\frac{3}{4} .(2)\\\\a_3 = -\frac{1}{2} +\frac{3}{4} .(3)\\\\.\\.\\.\\a_{12} = -\frac{1}{2} +\frac{3}{4} .(12)$

Entonces:

Entonces: $S_{12} =-\frac{1}{2} .(12)+\frac{3}{4} .(1)+\frac{3}{4} .(2)+\frac{3}{4} .(3)+...+\frac{3}{4} .(12)\\\\S_{12} =-\frac{1}{2} .(12)+\frac{3}{4} .(1+2+3+...+12)\\\\S_{12} =-6+\frac{3}{4} .(\frac{1+12}{2}).(12)\\\\S_{12} =-6+\frac{3}{4} .(\frac{13}{2}).(12)\\\\S_{12} =-6+\frac{117}{2}\\\\S_{12} =-6+58,5\\\\S_{12} =52,5$