Question

Calcule os termo de P.A (17,26,35,...197

Answer 1

Boa noite!

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Dados;

An → 197

N → ?

A1 → 17

R → a2-a1 → 26-17 = 9

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An=a1+(n-1)·r

197=17+(n-1)·9

197=17+9n-9

-9n=17-9-197

-9n=8-197

-9n=-189(-1)

9n=189

n=189/9

n=21

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$\textit{Sn}=\frac{\mathrm{(A1+An).n}}{\mathrm{2}}$

$\textit{S15}=\frac{\mathrm{(17+197).21}}{\mathrm{2}}$

$\textit{S15}=\frac{\mathrm{214\times21}}{\mathrm{2}}$

$\textit{S15}=\frac{\mathrm{4494}}{\mathrm{2}}$

$\mathbf{S15}=\boxed{\boxed{2247}}$

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Att;Guilherme Lima

Answer 2

an= a1 + (n - 1) • r

197= 17 + (n - 1) • 9

197= 17 + 9n - 9

197= 8 + 9n

9n + 8= 197

9n= 197 - 8

9n= 189

n= 189/9

n= 21

Sn= (a1 + an) • n/2

Sn= (17 + 197) • 21/2

Sn= 214 • 21/2

Sn= 107 • 21

Sn= 2247