Question

Uma PA tem a1 e r= 1. Determine a soma dos seus:
a) 10 primeiros termos
b) 20 primeiro termos

Answer 1

Vamos começar determinando o 10° termo e o 20° termo dessa PA utilizando a equação do termo geral:

$\boxed{a_n~=~a_1+(n-1)\,.\,r}\\\\\\\\a_{10}~=~a_1+(10-1)\,.\,r\\\\\\a_{10}~=~1+9\,.\,1\\\\\\a_{10}~=~1+9\\\\\\\boxed{a_{10}~=~10}\\\\\\\\a_{20}~=~a_1+(20-1)\,.\,r\\\\\\a_{20}~=~1+19\,.\,1\\\\\\a_{20}~=~1+19\\\\\\\boxed{a_{20}~=~20}$

Agora, utilizando a equação da soma dos termos de uma PA, podemos determinar as respostas para (a) e (b).

$S_{n}~=~\frac{(a_1+a_n)\,.\,n}{2}$

a)

$S_{10}~=~\frac{(a_1+a_{10})\,.\,10}{2}\\\\\\S_{10}~=~\frac{(1+10)\,.\,10}{2}\\\\\\S_{10}~=~(11)\,.\,5\\\\\\\boxed{S_{10}~=~55}$

b)

$S_{20}~=~\frac{(a_1+a_{20})\,.\,20}{2}\\\\\\S_{20}~=~\frac{(1+20)\,.\,20}{2}\\\\\\S_{20}~=~(21)\,.\,10\\\\\\\boxed{S_{20}~=~210}$

Answer 2

Resposta:

ertwq

Explicação passo a passo: