Question

calcule a soma dos múltiplos de 5 compreendidos entre 201 e 306

Answer 1

(205,210,... 305)

Dados

$a_{n}=305$

$a_{1}=205$

$r=5$

$\it{cálculo\,do\,número\,de\,termos:}$

$a_{n}=a_{1}+(n-1)r\\n=\dfrac{a_{n}-a_{1}}{r}+1$

$n=\dfrac{305-205}{5}+1=\dfrac{100}{5}+1\\n=20+1=21$

$s_{n}=\dfrac{n(a_{1}+a_{n})}{2}\\s_{21}=\dfrac{21(a_{1}+a_{21})}{2}$

$s_{21}=\dfrac{21(205+305)}{2}$

$s_{21}=\dfrac{21.\cancel{510}}{\cancel2}$

$s_{21}=21.255$

$\boxed{\boxed{\mathsf{s_{21}=5355}}}$