Question

Calcule a soma dos 40 primeiros termos da P.A. (2,6,.....)

Answer 1

Primeiro você terá que descobrir qual é o último termo dessa P.A.:


$a_{1}=2\\r=6\\n=40\\a_{n}=a_{40}=?\\\\a_{40} = a_{1} + (n-1)*r\to \\\\a_{40} = 2+ (40-1)*4\to\\\\ a_{40} =2+ 39*4\to \\\\a_{n} = 2+156\to \\\\ a_{40} =158$



$S_{n} = \frac{( a_{1} + a_{n})*n }{2} \to \\\\\\ S_{n} = \frac{( 2 + 158)*40 }{2} \to \\\\ S_{n} = \frac{160*40 }{2} \to \\\\ S_{n} = \frac{6400 }{2} \to \\\\ S_{n} = 3200$