Question

-8, -1, 6…. 41 Qual a soma dos termos dessa p.a?

Answer 1

Resposta:

132

Explicação passo a passo:

$a_{1} =-8\\\\ a_{2} =-1\\\\ r=a_{2}-a_{1} =-1-(-8)=-1+8=7\\\\ a_{n} =41\\\\ n=? \\\\ S_{n} =??$

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

$n=\frac{41-(-8)+7}{7}\\\\ n=\frac{41+8+7}{7}\\\\ n=\frac{49+7}{7} \\\\ n=\frac{56}{7} \\\\ n=8$

$S_{n} =\frac{(a_{1} +a_{n} )\times n}{2} \\\\ S_{n} =(a_{n} +a_{1} )\times \frac{n}{2} \\\\ S_{8} =(41 +(-8) )\times \frac{8}{2} \\\\ S_{8} =(41 -8 )\times 4 \\\\ S_{8} =33\times 4 \\\\ S_{8} = 132$