Question

Calcule a soma dos 100 primeiros termos da P.A (5.10.15)

Answer 1

$a_{1} =5 \\ \\ r= a_{2} - a_{1} =10-5=5 \\ \\ n=100 \\ \\ a_{n} = a_{1} +(n-1)r \\ \\ a_{100} =5+(100-1).5=5+99.5=5+495=500 \\ \\ S_{n} = \frac{( a_{1}+ a_{n} ).n}{2} \\ \\ S_{100} = \frac{( 5+ 500 ).100}{2} = \frac{505.100}{2} =25250$